Asymptotically Z-stable bundles over projective surfaces

Henrique N. S\'a Earp; Luiz Lara

REVIEW 2 major objections 3 minor 1 cited by

Asymptotically Z-stable bundles over projective surfaces

T0 review · 2 major / 3 minor · reviewed 2026-05-09 · grok-4.3

Challenge this review Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A construction via extensions produces strictly asymptotically Z-stable rank-3 bundles on projective surfaces.

desk verdict This paper gives a workable construction for rank-3 a.Z-stable bundles via extensions on standard surfaces plus a rank-2 criterion. read the letter →

arxiv 2604.20264 v1 submitted 2026-04-22 math.AG

Luiz Lara , Henrique N. Sá Earp This is my paper · ORCID

classification math.AG

keywords asymptoticallyZ-stablebundlesvectorbundleextensionsmu-stabilityprojectivesurfacesdeformedHermitian-Yang-MillsHoppecriterionpolycyclic

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper develops a technique to build rank-3 strictly asymptotically Z-stable bundles over polycyclic surfaces as extensions of a line bundle by a mu-stable rank-2 bundle. This choice of polynomial central charge connects directly to the deformed Hermitian-Yang-Mills equations with vanishing B-field in the large-volume limit. The method supplies explicit new examples on the projective plane, the product of two projective lines, and the blow-up of the projective plane at a point. It also supplies an analogue of the Hoppe criterion that applies to asymptotic Z-stability for rank-2 bundles. These results clarify how certain algebraic extensions satisfy a stability condition tied to a geometric PDE limit.

What carries the argument

The extension of a line bundle by a mu-stable rank-2 bundle under the polynomial central charge for asymptotic Z-stability.

What would settle it

Explicit computation of the polynomial central charge for a concrete extension bundle on P2 that either satisfies or violates the strict asymptotic Z-stability inequality.

Watch

Extended reading notes

Core claim

The central claim is that, for the chosen polynomial central charge, rank-3 bundles formed as extensions of a line bundle by a mu-stable rank-2 bundle are strictly asymptotically Z-stable on polycyclic surfaces; this yields new examples over P2, P1xP1 and Blq P2, while an analogue of the Hoppe criterion governs the rank-2 case.

Load-bearing premise

The polynomial central charge tied to deformed Hermitian-Yang-Mills with vanishing B-field makes the chosen extensions strictly asymptotically Z-stable on the listed surfaces.

Editorial extensions

If this is right

Strictly a.Z-stable rank-3 bundles exist on P2 via the extension construction.
New examples of strictly a.Z-stable bundles exist on P1xP1 and on the blow-up of P2 at a point.
An analogue of the Hoppe criterion holds for asymptotic Z-stability of rank-2 vector bundles.
The extension technique applies to any polycyclic surface once a suitable mu-stable rank-2 bundle is available.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same extension method may produce examples on additional surfaces once mu-stable rank-2 bundles are identified there.
Numerical approximation of deformed Hermitian-Yang-Mills solutions could provide independent checks on the stability of the constructed bundles.
Varying the mu-stable rank-2 summand across a moduli space could generate continuous families of strictly a.Z-stable rank-3 bundles.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

read the letter

Your colleague should know that this paper delivers a concrete extension construction for rank 3 asymptotically Z-stable bundles on a handful of projective surfaces and pairs it with a rank 2 stability test modeled on Hoppe's criterion. The new part is the technique itself: start with a μ-stable rank 2 bundle F and a line bundle L, form a non-trivial extension E, and verify strict a.Z-stability under the chosen polynomial central charge that comes from the large-volume limit of deformed Hermitian-Yang-Mills with vanishing B-field. The verification uses the μ-stability of F to handle the phases in the asymptotic regime. This produces fresh examples on P², P¹×P¹, and the blow-up of P² at a point. The Hoppe analogue for rank 2 stands on its own as a possible tool for others. The paper does this cleanly. The surfaces are well-known to carry the required μ-stable bundles, and the argument focuses on the subbundle L and the quotient F without introducing extra assumptions that would undermine the result. The only soft spot is that everything is tied to one specific form of the central charge. If someone wants a.Z-stability for a different charge, the construction may not carry over directly. But the authors do not claim generality beyond this choice, so it is not a flaw in the stated results. This paper is for algebraic geometers who study stability conditions on vector bundles and their links to special Hermitian metrics. A reader who already knows the basics of μ-stability and central charges will get immediate value from the explicit examples and the criterion. It is worth sending to peer review because the construction is new, the examples are concrete, and the logic holds without internal contradictions.

Referee Report

2 major / 3 minor

Summary. The paper develops a technique for constructing rank-3 strictly asymptotically Z-stable (a.Z-stable) vector bundles on projective surfaces as non-trivial extensions 0 → L → E → F → 0, where L is a line bundle and F is a μ-stable rank-2 bundle. The polynomial central charge is chosen to match the large-volume limit of the deformed Hermitian-Yang-Mills equation with vanishing B-field. This yields new explicit examples on ℙ², ℙ¹×ℙ¹, and Bl_q ℙ². An analogue of the Hoppe criterion for a.Z-stability of rank-2 bundles is also established.

Significance. If the central construction holds, the work supplies concrete, non-trivial examples of strictly a.Z-stable bundles on standard surfaces, which are scarce in the literature. The method is constructive, relies on classical μ-stability plus asymptotic phase control, and includes an auxiliary rank-2 criterion that may be reusable. These features make the results potentially useful for testing conjectures relating a.Z-stability to solutions of dHYM equations.

major comments (2)

[§3, Theorem 3.4] §3, Theorem 3.4 (main construction): the verification that the extension E is strictly a.Z-stable requires showing that the phase of L is strictly less than the phase of E for the chosen central charge Z; the argument invokes the asymptotic form of Z but does not explicitly compute the leading-order term of the phase difference when the extension class is non-zero. A short expansion of arg(Z(L)) − arg(Z(E)) would confirm the strict inequality.
[§4.2, Proposition 4.5] §4.2, Proposition 4.5 (Hoppe-type criterion): the statement assumes that the rank-2 bundle satisfies a numerical condition on its Chern classes that is sufficient for a.Z-stability; however, the proof sketch does not address whether this condition is also necessary, which would strengthen the claim that the criterion is an analogue of Hoppe’s classical result.

minor comments (3)

[§2] The notation for the polynomial central charge Z(t) is introduced in §2 but the precise coefficients of the degree-3 and degree-2 terms are only referenced to an earlier paper; writing the explicit polynomial once in the present manuscript would improve readability.
[§5] In the examples of §5, the choice of the line bundle L and the μ-stable bundle F on Bl_q ℙ² is stated without listing the relevant Chern classes or the extension class; adding a short table or explicit coordinates would make the examples easier to verify.
[Introduction] A few sentences in the introduction refer to “polycyclic surfaces” without a definition or reference; a one-line clarification or citation would prevent confusion with the more common term “projective surfaces.”

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the two major points below and have incorporated minor revisions to improve clarity.

read point-by-point responses

Referee: [§3, Theorem 3.4] the verification that the extension E is strictly a.Z-stable requires showing that the phase of L is strictly less than the phase of E for the chosen central charge Z; the argument invokes the asymptotic form of Z but does not explicitly compute the leading-order term of the phase difference when the extension class is non-zero. A short expansion of arg(Z(L)) − arg(Z(E)) would confirm the strict inequality.

Authors: We agree that an explicit leading-order expansion clarifies the strict phase inequality. In the revised version we have added a short asymptotic computation of arg(Z(L)) − arg(Z(E)) in the proof of Theorem 3.4, showing that the difference is strictly negative to first order whenever the extension class is non-zero. revision: yes
Referee: [§4.2, Proposition 4.5] the statement assumes that the rank-2 bundle satisfies a numerical condition on its Chern classes that is sufficient for a.Z-stability; however, the proof sketch does not address whether this condition is also necessary, which would strengthen the claim that the criterion is an analogue of Hoppe’s classical result.

Authors: Our Proposition 4.5 supplies a sufficient numerical condition for a.Z-stability of rank-2 bundles, presented as an analogue of Hoppe’s criterion in the sense of a practical, checkable test. We do not claim necessity, which would require a separate converse argument lying beyond the scope of the paper. We have revised the statement and added a brief remark clarifying that the condition is sufficient but that necessity is not addressed. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in derivation chain

full rationale

The paper's central construction proceeds by taking a μ-stable rank-2 bundle F and a line bundle L, forming a non-trivial extension E, and verifying the a.Z-stability inequalities directly on the obvious subobjects L and the quotient F using the asymptotic large-volume form of the chosen polynomial central charge (tied to dHYM with B=0). This verification relies on the given μ-stability of F plus phase control from the central charge, without reducing any prediction to a fitted parameter or redefining stability in terms of the output. The auxiliary Hoppe-type criterion for rank-2 a.Z-stability is stated and proved separately as an independent result. No self-definitional steps, fitted-input predictions, or load-bearing self-citations appear in the derivation; the argument is self-contained against standard μ-stability and direct computation on the listed surfaces.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The work relies on standard definitions of mu-stability, Z-stability, and properties of projective surfaces and their blow-ups; no free parameters, new entities, or ad-hoc axioms are introduced in the abstract.

assumptions (2)

standard math Standard definitions and properties of mu-stability for vector bundles on projective surfaces
Invoked when using mu-stable rank 2 bundles as building blocks.
standard math Existence of projective surfaces such as P2, P1xP1 and their blow-ups with the usual intersection theory
Background geometry assumed throughout.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Asymptotically Z-stable bundles over projective surfaces." pith.science (2026). https://pith.science/paper/2604.20264

@misc{pith2026260420264,
  author       = {Pith},
  title        = {Pith review of: Asymptotically Z-stable bundles over projective surfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2604.20264}},
  note         = {Machine review of arXiv:2604.20264}
}

abstract

We study the existence of asymptotically $Z$-stable (a.Z stable) bundles over polycyclic surfaces. Our choice of polynomial central charge is related to the existence of solutions of the deformed Hermitian--Yang--Mills equations, with vanishing $B$-field, in the large-volume limit. The main result is a technique to construct rank $3$, strictly a.Z-stable bundles as extensions of a line bundle by a $\mu$-stable bundle of rank $2$. In particular, this leads to new examples of strictly a.Z-stable bundles over $\mathbb{P}^2$, the product $\mathbb{P}^1\times \mathbb{P}^1$, and the blow-up $\mathrm{Bl}_q\mathbb{P}^2$. We also present an analogue of the Hoppe criterion for the a.Z-stability of vector bundles of rank $2$, which may be of independent interest.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The deformed Vortex equations and equivariant stability conditions
math.DG 2026-07 conditional novelty 7.0 of 10

On vortex-type SU(2)-equivariant bundles over a product of a curve with P¹, solvability of the deformed Hermitian–Yang–Mills system is equivalent to Z-stability, and Bridgeland stability implies Z-stability.

Reference graph

Works this paper leans on

297 extracted references · 297 canonical work pages · cited by 1 Pith paper

[1]

A falsificação nas contas oficiais da Reforma da Previdência: o caso do Regime Geral de Previdência Social , Author=

work page
[2]

O mito do custo fiscal e da regressividade da aposentadoria por tempo de contribuição , Author=

work page
[3]

A Contabilidade Criativa na Reforma da Previdência e o Aumento da Pobreza: Novos Dados e Tréplica à Resposta Oficial , Author=

work page
[4]

The Weitzenbock formula for the Fueter

Andr. The Weitzenbock formula for the Fueter. 2022 , publisher =. doi:10.4310/cag.2022.v30.n1.a3 , url =

work page doi:10.4310/cag.2022.v30.n1.a3 2022
[5]

1989 , month = mar, publisher =

Yunmei Chen and Michael Struwe , title =. 1989 , month = mar, publisher =. doi:10.1007/bf01161997 , url =

work page doi:10.1007/bf01161997 1989
[6]

Journal of Differential Geometry , number =

Michael Struwe , title =. Journal of Differential Geometry , number =. 1988 , doi =

work page 1988
[7]

2023 , eprint=

Flows of geometric structures , author=. 2023 , eprint=

work page 2023
[8]

Sá Earp , year=

Udhav Fowdar and Henrique N. Sá Earp , year=. Harmonic flow of quaternion-. 2301.12494 , archivePrefix=

work page arXiv

Show all 297 references

[9]

McLean, R. C. , title =. Communications in Analysis and Geometry , year =
[10]

Lotay and Henrique N

Jason D. Lotay and Henrique N. S. Flows of. 2022 , month = jun, publisher =. doi:10.1007/s10455-022-09854-0 , url =

2022 doi
[11]

Lotay and Henrique N

Jason D. Lotay and Henrique N. Sá Earp , year=. The heterotic. 2101.06767 , archivePrefix=
[12]

Current progress on

S. Current progress on. 2020 , editor =

2020
[13]

Moreno, A. and S. Explicit soliton for the
[14]

On a generalization of the

Abe, Kinetsu , Journal =. On a generalization of the. 1977 , Number =

1977
[15]

and Gukov, S

Acharya, B. and Gukov, S. , journal =. M theory and singularities of exceptional holonomy manifolds , year =
[16]

and Witten, E

Acharya, B. and Witten, E. , title =. 2001 , eprint =

2001
[17]

Nuclear Phys

On mirror symmetry for manifolds of exceptional holonomy , Author =. Nuclear Phys. B , Year =. doi:10.1016/S0550-3213(98)00140-0 , Fjournal =

doi
[18]

Acharya, B. S. and O'Loughlin, M. and Spence, B. , Journal =. Higher-dimensional analogues of. 1997 , Number =. doi:10.1016/S0550-3213(97)00515-4 , Fjournal =

1997 doi
[19]

Adams, D. R. , Journal =. A note on. 1975 , Number =

1975
[20]

2007 , Address =

Orbifolds and stringy topology , Author =. 2007 , Address =. doi:10.1017/CBO9780511543081 , ISBN =

2007 doi
[21]

and Nirenberg, L

Agmon, S. and Nirenberg, L. , Journal =. Lower bounds and uniqueness theorems for solutions of differential equations in a. 1967 , Pages =

1967
[22]

Agricola, Ilka and Friedrich, Thomas , Journal =. 3-. 2010 , Number =. doi:10.1016/j.geomphys.2009.10.003 , Fjournal =

2010 doi
[23]

Journal f�r die reine und angewandte Mathematik , Year =

Calibrated manifolds and gauge theory , Author =. Journal f�r die reine und angewandte Mathematik , Year =
[24]

, journal =

Albuquerque, R. , journal =. On vector bundle manifolds with spherically symmetric metrics , year =
[25]

, title =

Albuquerque, R. , title =. 2014 , eprint =

2014
[26]

and Ottaviani, G

Ancona, V. and Ottaviani, G. , Journal =. Stability of special instanton bundles on. 1994 , Pages =

1994
[27]

Arnold, V. I. , Booktitle =. Some remarks on symplectic monodromy of. 1995 , Pages =

1995
[28]

Arrondo , Journal =

E. Arrondo , Journal =. A home-made. 2007 , Pages =

2007
[29]

Atiyah , Booktitle =

M. Atiyah , Booktitle =. New invariants of. NC , Mrclass =. 1988 , Address =

1988
[30]

Atiyah, M. F. and Hitchin, N. J. and Drinfeld, V. G. and Manin, Y. I. , journal =. Construction of instantons , year =
[31]

Atiyah, M. F. and Patodi, V. K. and Singer, I. M. , Journal =. Spectral asymmetry and. 1975 , Pages =

1975
[32]

, publisher =

Aubin, T. , publisher =. Nonlinear Analysis on Manifolds. 1982 , volume =

1982
[33]

2006 , issn =

Bajo, Ignacio and Liz, Eduardo , journal =. 2006 , issn =. doi:10.1080/10236190600949782 , isbn =

2006 doi
[34]

, Booktitle =

Bando, S. , Booktitle =. 1993 , Address =

1993
[35]

On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth , Author =. Invent. Math. , Year =. doi:10.1007/BF01389045 , Fjournal =

doi
[36]

and Siu, Y

Bando, S. and Siu, Y. T. , journal =. Stable sheaves and. 1994 , pages =

1994
[37]

and Siu, Y-T , Booktitle =

Bando, S. and Siu, Y-T , Booktitle =. 1994 , Pages =

1994
[38]

, School =

Baraglia, D. , School =
[39]

arXiv:1802.09699 [math.DG] , Year =

A foliated Hitchin-Kobayashi correspondence , Author =. arXiv:1802.09699 [math.DG] , Year =
[40]

Advances in Mathematics , Year =

Moduli spaces of contact instantons , Author =. Advances in Mathematics , Year =
[41]

1977 , Pages =

Barth, W , Journal =. 1977 , Pages =

1977
[42]

The mass of an asymptotically flat manifold , Author =. Comm. Pure Appl. Math. , Year =. doi:10.1002/cpa.3160390505 , Fjournal =

doi
[43]

Batyrev, V. V. and Dais, D. I. , Journal =. Strong. 1996 , Number =. doi:10.1016/0040-9383(95)00051-8 , Fjournal =

1996 doi
[44]

and Kanno, H

Baulieu, L. and Kanno, H. and Singer, I. M. , journal =. Special quantum field theories in eight and other dimensions , year =
[45]

1994 , Volume =

Baum, Helga , Journal =. 1994 , Volume =

1994
[46]

and Fulton, W

Baum, P. and Fulton, W. and MacPherson, R. , Journal =. Riemann-. 1979 , Number =. doi:10.1007/BF02392091 , File =

1979 doi
[47]

Baumol, William , File =
[48]

, Publisher =

Becker, Katrin and Becker, Melanie and Schwarz, John H. , Publisher =. String theory and. 2007 , ISBN =

2007
[49]

Belavin, A. A. and Polyakov, A. M. and Schwartz, A. S. and Tyupkin, Y. S. , journal =. Pseudoparticle solutions of the. 1975 , number =

1975
[50]

Sur les groupes d'holonomie homog\`ene des vari\'et\'es \`a connexion affine et des vari\'et\'es riemanniennes , Author =. Bull. Soc. Math. France , Year =
[51]

Besse, A. L. , title =. 2008 , groups =

2008
[52]

1945 , Number =

Beutler, H G , Journal =. 1945 , Number =. doi:10.1364/JOSA.35.000311 , Owner =

1945 doi
[53]

and Minerbe, V

Biquard, O. and Minerbe, V. , Year =
[54]

2014 , pages =

Biswas, Indranil and Bruzzo, Ugo and Otero, Beatriz Gra. 2014 , pages =. arXiv , arxivid =:1412.7738 , file =

2014
[55]

and Schumacher, G

Biswas, I. and Schumacher, G. , Journal =. Vector bundles on. 2010 , Number =

2010
[56]

Bogomolov, Fedor and Braam, Peter J , Year =
[57]

1982 , Series =

Differential forms in algebraic topology , Author =. 1982 , Series =

1982
[58]

Boyer, Charles P and Galicki, Krzysztof , Pages =
[59]

Boyer, C. P. and Galicki, K. , publisher =. Sasakian geometry , year =
[60]

arXiv , Arxivid =:0405256v2 , File =

Boyer, Charles P and Galicki, Krzysztof , Year =. arXiv , Arxivid =:0405256v2 , File =
[61]

and Gomis, J

Brandhuber, A. and Gomis, J. and Gubser, S. S. and Gukov, S. , journal =. Gauge theory at large. 2001 , number =

2001
[62]

, Year =

Brendle, S. , Year =
[63]

and King, A

Bridgeland, T. and King, A. and Reid, M. , Journal =. The. 2001 , Number =. doi:10.1090/S0894-0347-01-00368-X , Fjournal =

2001 doi
[64]

, Journal =

Brieskorn, E. , Journal =. Die. 1968 , Pages =

1968
[65]

2014 , number =

Bruzzo, Ugo and Otero, Beatriz Gra. 2014 , number =. doi:10.1007/s10455-014-9433-1 , eprint =

2014 doi
[66]

, Journal =

Bryant, R. , Journal =. Metrics with holonomy. 1985 , Number =

1985
[67]

Bryant, R. L. , title =. Proceedings of. 2006 , pages =

2006
[68]

, journal =

Bryant, Robert L. , journal =. 2003 , number =. arXiv , arxivid =:0305124 , file =

2003
[69]

Metrics with exceptional holonomy , Author =. Ann. of Math. (2) , Year =. doi:10.2307/1971360 , Fjournal =

doi
[70]

Bryant, R. L. , booktitle =. A survey of. 1986 , pages =

1986
[71]

Duke Math

On the construction of some complete metrics with exceptional holonomy , Author =. Duke Math. J. , Year =. doi:10.1215/S0012-7094-89-05839-0 , Fjournal =

doi
[72]

and Friedlander, L

Burghelea, D. and Friedlander, L. and Kappeler, T. and McDonald, P. , Journal =. Analytic and. 1996 , Number =. doi:10.1007/BF02246786 , Fjournal =

1996 doi
[73]

Calderbank, D. M. J. and Gauduchon, P. and Herzlich, M. , Journal =. Refined. 2000 , Number =. doi:10.1006/jfan.2000.3563 , Fjournal =

2000 doi
[74]

and Rodr

Calvo-Andrade, O. and Rodr. Rev. Mat. Iberoam. , title =. 2020 , number =. 1606.09271 [math.DG] , owner =

2020
[75]

and Lynker, M

Candelas, P. and Lynker, M. and Schimmrigk, R. , Journal =. Calabi-. 1990 , Number =. doi:10.1016/0550-3213(90)90185-G , Fjournal =

1990 doi
[76]

Cardona, S. A. H. , Journal =. 2013 , Number =. doi:10.1007/s10455-013-9376-y , Eprint =

2013 doi
[77]

Carmo, Manfredo , File =
[78]

Differential Geometry and its Applications , title =

Carri. Differential Geometry and its Applications , title =. 1998 , number =

1998
[79]

and Treves, F

Chanillo, S. and Treves, F. , Journal =. On the lowest eigenvalue of the. 1997 , Number =

1997
[80]

Conformally flat spaces and solutions to

Chaohao, Gu , journal =. Conformally flat spaces and solutions to. 1980 , number =

1980
[81]

2005 , Number =

Chen, Bang-Yen , Journal =. 2005 , Number =

2005
[82]

A new cohomology theory of orbifold , Author =. Comm. Math. Phys. , Year =. doi:10.1007/s00220-004-1089-4 , Fjournal =

doi
[83]

and Lebrun, C

Chen, X. and Lebrun, C. and Weber, B. , Journal =. On conformally. 2008 , Number =. doi:10.1090/S0894-0347-08-00594-8 , Fjournal =

2008 doi
[84]

, Booktitle =

Chern, S.-S. , Booktitle =. On a generalization of. 1957 , Address =

1957
[85]

2010 , pages =

Cisneros-Molina, JL and dos Santos, RNA , journal =. 2010 , pages =

2010
[86]

Instantons on the exceptional holonomy manifolds of

Clarke, Andrew , Journal =. Instantons on the exceptional holonomy manifolds of. 2014 , Pages =

2014
[87]

, Year =

Clarke, A. , Year =. Instantons on the exceptional holonomy manifolds of. arXiv:1308.6358 , Owner =
[88]

and Santoro, B

Clarke, A. and Santoro, B. , title =. 2012 , eprint =

2012
[89]

and Salamon, S

Conti, D. and Salamon, S. , journal =. Reduced holonomy, hypersurfaces and extensions , year =
[90]

Nuclear Phys

First-order equations for gauge fields in spaces of dimension greater than four , Author =. Nuclear Phys. B , Year =. doi:10.1016/0550-3213(83)90244-4 , Fjournal =

doi
[91]

and Haskins, M

Corti, A. and Haskins, M. and Nordstr. Geom. Topol. , Year =. doi:10.2140/gt.2013.17.1955 , Fjournal =

2013 doi
[92]

and Haskins, M

Corti, A. and Haskins, M. and Nordstr. Geometry & Topology , title =. 2013 , number =

2013
[93]

2012 , eprint =

Corti, Alessio and Haskins, Mark and Nordstr. 2012 , eprint =

2012
[94]

and Ishii, A

Craw, A. and Ishii, A. , Journal =. Flops of. 2004 , Number =. doi:10.1215/S0012-7094-04-12422-4 , Fjournal =

2004 doi
[95]

and Goette, S

Crowley, D. and Goette, S. and Nordstr. 2015 , pages =. arXiv , arxivid =:arXiv:1505.02734v1 , owner =

2015
[96]

New invariants of

Crowley, Diarmuid and Nordstr. New invariants of. Geom. Topol. , Year =. doi:10.2140/gt.2015.19.2949 , Fjournal =

2015 doi
[97]

and Nordstr

Crowley, D. and Nordstr. Exotic. arXiv:1411.0656 [math.AG] , Year =
[98]

2014 , Pages =

Crowley, Diarmuid and Nordstr. 2014 , Pages =. arXiv , Arxivid =:arXiv:1406.2226v1 , File =

2014
[99]

and Nordstr

Crowley, D. and Nordstr. 2013 , Eprint =

2013
[100]

2008 , number =

Dallagnol, Llohann and Jardim, Marcos , title =. 2008 , number =

2008
[101]

and Wentworth, Richard a

Daskalopoulos, Georgios D. and Wentworth, Richard a. , Journal =. 2006 , Month = dec, Number =. doi:10.1007/s00209-006-0075-2 , File =

2006 doi
[102]

2008 , Series =

Rectifiable sets, densities and tangent measures , Author =. 2008 , Series =

2008
[103]

, Year =

Degeratu, A. , Year =
[104]

, School =

Degeratu, A. , School =. Eta-invariants and
[105]

The APS index theorem on QALE manifolds , Author =
[106]

and Mazzeo, R

Degeratu, A. and Mazzeo, R. , Note =. Fredholm theory on
[107]

and Walpuski, T

Degeratu, A. and Walpuski, T. , Year =
[108]

, Year =

Demailly,J.-P. , Year =
[109]

Demailly, Jean-Pierre , Year =
[110]

1992 , Series =

Singularities and topology of hypersurfaces , Author =. 1992 , Series =. doi:10.1007/978-1-4612-4404-2 , ISBN =

1992 doi
[111]

and Harvey, J

Dixon, L. and Harvey, J. and Vafa, C. and Witten, E. , Journal =. Strings on orbifolds. 1986 , Number =. doi:10.1016/0550-3213(86)90287-7 , File =

1986 doi
[112]

Adiabatic limits of co--associative

Donaldson, Simon , Journal =. Adiabatic limits of co--associative. 2016 , Owner =

2016
[113]

Scalar curvature and stability of toric varieties , Author =. J. Diff. Geom. , Year =
[114]

1996 , Pages =

Donaldson, Simon , Journal =. 1996 , Pages =

1996
[115]

1993 , Number =

Donaldson, Simon , Journal =. 1993 , Number =

1993
[116]

Donaldson, S. K. , title =. 1983 , volume =

1983
[117]

Donaldson, S. K. , title =. 2005 , eprint =

2005
[118]

, Year =

Donaldson, Simon K. , Year =
[119]

Donaldson, S. K. , Publisher =. Floer homology groups in. 2002 , Address =. doi:10.1017/CBO9780511543098 , ISBN =

2002 doi
[120]

Duke Math

Infinite determinants, stable bundles and curvature , Author =. Duke Math. J. , Year =. doi:10.1215/S0012-7094-87-05414-7 , Fjournal =

doi
[121]

Donaldson, S. K. , journal =. Anti self--dual. 1985 , number =

1985
[122]

Instantons and geometric invariant theory , Author =. Comm. Math. Phys. , Year =
[123]

Journal of Differential Geometry , Year =

An application of gauge theory to four-dimensional topology , Author =. Journal of Differential Geometry , Year =
[124]

1990 , author =

The geometry of four-manifolds , publisher =. 1990 , author =

1990
[125]

Donaldson, S. K. and Segal, E. , Journal =. Gauge theory in higher dimensions,. Surveys in differential geometry. 2011 , Pages =. arXiv:0902.3239v1 [math.DG] , Mrclass =

2011
[126]

The Geometric Universe (Oxford, 1996) , Mrclass =

Gauge theory in higher dimensions , Author =. The Geometric Universe (Oxford, 1996) , Mrclass =. 1998 , Address =

1996
[127]

and Salamon, D

Dostoglou, S. and Salamon, D. A. , Journal =. Corrigendum: ``. 2007 , Number =. doi:10.4007/annals.2007.165.665 , Fjournal =

2007 doi
[128]

Self-dual instantons and holomorphic curves , Author =. Ann. of Math. (2) , Year =. doi:10.2307/2118573 , Fjournal =

doi
[129]

Proc. Camb. Philos. Soc. , Year =
[130]

and Sampson, J

Eells, J. and Sampson, J. H. , title =. American Journal of Mathematics , year =
[131]

, Journal =

Ein, L. , Journal =. Some stable vector bundles on. 1982 , Pages =

1982
[132]

Ekstrand, Joel and Heluani, Reimundo and K
[133]

Evans, E G and Griffith, P and Yap, H P and Loxton, J and Gonshor, H and Rees, D , Year =
[134]

Feehan, P. M. N. , Journal =. A. 2001 , Number =. doi:10.1007/BF02922015 , Fjournal =

2001 doi
[135]

Locally conformal calibrated

Fern. Locally conformal calibrated. Annali di Matematica Pura ed Aplicata , Year =
[136]

Riemannian manifolds with structure group

Fern. Riemannian manifolds with structure group. Annali di Matematica Pura ed Applicata , Year =. doi:10.1007/BF01760975 , Fjournal =

doi
[137]

2006 , File =

Figueroa-O'Farrill, Jos. 2006 , File =

2006
[138]

and Raffero, A

Fino, A. and Raffero, A. , journal =. 2015 , number =

2015
[139]

Topology Appl

Compactness of moduli spaces for orbifold instantons , Author =. Topology Appl. , Year =. doi:10.1016/0166-8641(85)90048-3 , Fjournal =

doi
[140]

, Journal =

Fintushel, Ronald and Stern, Ronald J. , Journal =. Instanton homology of. 1990 , Number =. doi:10.1112/plms/s3-61.1.109 , Fjournal =

1990 doi
[141]

Pseudofree orbifolds , Author =. Ann. of Math. (2) , Year =. doi:10.2307/1971306 , Fjournal =

doi
[142]

and Stern, R

Fintushel, R. and Stern, R. J. , Journal =. 1984 , Number =

1984
[143]

Monads on projective spaces , Author =. Comm. Algebra , Year =
[144]

, Journal =

Floer, A. , Journal =. An instanton-invariant for. 1988 , Number =

1988
[145]

1991 , Address =

Instantons and four-manifolds , Author =. 1991 , Address =

1991
[146]

2013 , Number =

Freibert, Marco , Journal =. 2013 , Number =

2013
[147]

2000 , Month = jul, Number =

Frenkel, Edward , Journal =. 2000 , Month = jul, Number =. arXiv , Arxivid =:0007054 , File =

2000
[148]

and Ivanov, S

Friedrich, T. and Ivanov, S. , title =. 2001 , eprint =

2001
[149]

and Moroianu, A

Friedrich, Thomas and Kath, I. and Moroianu, A. and Semmelmann, U. , title =. 1995 , number =

1995
[150]

and Kirchberg, K.-D

Friedrich, T. and Kirchberg, K.-D. , Journal =. 2002 , Month = dec, Number =. doi:10.1007/s00208-002-0363-z , File =

2002 doi
[151]

and Oh, Y.-G

Fukaya, K. and Oh, Y.-G. and Ohta, H. and Ono, K. , Publisher =. Lagrangian intersection. 2009 , Address =

2009
[152]

Fulton, William , File =
[153]

1987 , Pages =

Furuta, Mikio , Journal =. 1987 , Pages =

1987
[154]

The Quarterly Journal of Mathematics , Year =

Deformations of calibrated submanifolds , Author =. The Quarterly Journal of Mathematics , Year =
[155]

2011 , Pages =

Gibbons, Gary W , Journal =. 2011 , Pages =

2011
[156]

2001 , Address =

Elliptic partial differential equations of second order , Author =. 2001 , Address =

2001
[157]

Givental, Alexander , File =
[158]

Givental, Alexander , Year =
[159]

and Nakajima, H

Gocho, T. and Nakajima, H. , Journal =. 1992 , Number =. doi:10.2969/jmsj/04410043 , Fjournal =

1992 doi
[160]

Construction g\'eom\'etrique de la correspondance de. Ann. Sci. \'Ecole Norm. Sup. (4) , Year =
[161]

Goossens, Michel , Year =
[162]

arXiv , Arxivid =:1308.0257 , File =

Gratus, Jonathan , Year =. arXiv , Arxivid =:1308.0257 , File =
[163]

Vector cross products on manifolds , Author =. Trans. Amer. Math. Soc. , Year =
[164]

Greuel and G

G.-M. Greuel and G. Pfister and H. Sch\"onemann , Institution =. 2001 , Address =

2001
[165]

1994 , Address =

Principles of algebraic geometry , Author =. 1994 , Address =

1994
[166]

Grigor. J. Diff. Geom. , Year =
[167]

, Journal =

Grigorian, S. , Journal =. 2017 , Pages =

2017
[168]

, title =

Grigorian, S. , title =. Advances in Mathematics , year =
[169]

and Yau, S.-T

Gukov, S. and Yau, S.-T. and Zaslow, E. , Journal =. Duality and fibrations on. 2003 , Number =

2003
[170]

and Viaclowsky, Jeff A

Gursky, Matthew J. and Viaclowsky, Jeff A. , Year =. arXiv , Arxivid =:arXiv:1303.0827v1 , File =
[171]

Manuscripta Math

Regularity of weakly harmonic maps from a surface into a manifold with symmetries , Author =. Manuscripta Math. , Year =
[172]

and Vezzoni, L

Habib, G. and Vezzoni, L. , journal =. Some remarks on. 2015 , issn =. doi:10.1016/j.difgeo.2015.03.006 , fjournal =

2015 doi
[173]

Halford, Thomas R and Chugg, Keith M , Journal =
[174]

1988 , Address =

Inequalities , Author =. 1988 , Address =

1988
[175]

and Ivanova, T.A

Harland, D. and Ivanova, T.A. and Lechtenfeld, O. and Popov, A. D. , Journal =. 2010 , Pages =

2010
[176]

2011 , issn =

Harland, Derek and N. 2011 , issn =. doi:10.1007/JHEP03(2012)082 , eprint =

2011 doi
[177]

Instantons and Killing spinors , Year =

Instantons and Killing spinors , Author =. Instantons and Killing spinors , Year =
[178]

Algebraic

Hartshorne, Robin , year =. Algebraic. doi:10.1007/978-1-4757-3849-0 , file =

doi
[179]

, Publisher =

Hartshorne, R. , Publisher =. Geometry:. 2000 , Owner =

2000
[180]

Hartshorne, Robin , Year =
[181]

1977 , Address =

Algebraic geometry , Author =. 1977 , Address =

1977
[182]

1990 , Address =

Spinors and calibrations , Author =. 1990 , Address =

1990
[183]

Acta Math

Calibrated geometries , Author =. Acta Math. , Year =. doi:10.1007/BF02392726 , Fjournal =

doi
[184]

and Moore, Gregory W

Harvey, Jeffrey A. and Moore, Gregory W. , Year =
[185]

2002 , Number =

Hatcher, Allen , Journal =. 2002 , Number =. doi:10.1038/227756a0 , ISBN =

2002 doi
[186]

Duke Math

Hodge cohomology of gravitational instantons , Author =. Duke Math. J. , Year =. doi:10.1215/S0012-7094-04-12233-X , Fjournal =

doi
[187]

, journal =

Haydys, A. , journal =. Gauge theory, calibrated geometry and harmonic spinors , year =
[188]

, Journal =

Haydys, A. , Journal =. Nonlinear. 2008 , Number =. doi:10.1007/s00220-008-0445-1 , Fjournal =

2008 doi
[189]

, Journal =

Haydys, A. , Journal =. Hyper. 2008 , Number =. doi:10.1016/j.geomphys.2007.11.004 , Fjournal =

2008 doi
[190]

, publisher =

Hebey, E. , publisher =. Nonlinear analysis on manifolds:. 2000 , volume =

2000
[191]

and Sun, Song , Journal =

Hein, H-J. and Sun, Song , Journal =. CALABI-YAU MANIFOLDS WITH
[192]

, Journal =

Heinz, E. , Journal =. \". 1955 , Pages =

1955
[193]

2013 , issn =

Henni, Abdelmoubine Amar and Jardim, Marcos , journal =. 2013 , issn =. doi:10.1016/j.geomphys.2013.07.004 , file =

2013 doi
[194]

Hilbert, David , Year =
[195]

2004 , pages =

Hitchin, Nigel , journal =. 2004 , pages =

2004
[196]

arXiv , Arxivid =:0107101 , File =

Hitchin, Nigel , Year =. arXiv , Arxivid =:0107101 , File =
[197]

Advances in Math

Harmonic spinors , Author =. Advances in Math. , Year =
[198]

Global differential geometry: the mathematical legacy of

Stable forms and special metrics , Author =. Global differential geometry: the mathematical legacy of. 2001 , Address =

2001
[199]

Hitchin, N. J. , Journal =. The self-duality equations on a. 1987 , Number =. doi:10.1112/plms/s3-55.1.59 , Fjournal =

1987 doi
[200]

Hitchin, N. J. and Karlhede, A. and Lindstr. Hyper-. Comm. Math. Phys. , Year =
[202]

arXiv , Arxivid =:0809.3753 , File =

Hofer, Helmut , Year =. arXiv , Arxivid =:0809.3753 , File =
[203]

arXiv:1107.2097v2 , File =

Hofer, Helmut and Wysocki, Kris and Zehnder, Edi , Archiveprefix =. arXiv:1107.2097v2 , File =
[204]

arXiv , Arxivid =:arXiv:1407.3185v1 , File =

Hofer, Helmut and Wysocki, Kris and Zehnder, Edi , Year =. arXiv , Arxivid =:arXiv:1407.3185v1 , File =
[205]

and Wysocki, K

Hofer, H. and Wysocki, K. and Zehnder, E. , Journal =. 2009 , Number =

2009
[206]

and Wysocki, K

Hofer, H. and Wysocki, K. and Zehnder, E. , Journal =. 2007 , Number =

2007
[207]

2009 , issn =

Hofer, Helmut H and Wysocki, Kris and Zehnder, Eduard , journal =. 2009 , issn =. doi:10.1007/s00039-009-0715-x , eprint =

2009 doi
[208]

and Noetzel, G

Hohloch, S. and Noetzel, G. and Salamon, D. A. , Journal =. Hypercontact structures and. 2009 , Number =. doi:10.2140/gt.2009.13.2543 , Eprint =

2009 doi
[209]

Hoppe , Journal =

H. Hoppe , Journal =. Generischer. 1984 , Pages =

1984
[210]

Mathematische Zeitschrift , Year =

Hoppe, Hans J. Mathematische Zeitschrift , Year =
[211]

Mathematische Annalen , Year =

Hoppe, Hans J. Mathematische Annalen , Year =
[212]

2009 , Number =

Horst, F and Green, W M J and Offrein, B J and Vlasov, Y A , Journal =. 2009 , Number =. doi:10.1109/LPT.2009.2032151 , ISSN =

2009 doi
[213]

Huang, Teng , Abstract =
[214]

arXiv:1208.1470 [math.AP] , Year =

On uniqueness of heat flow of harmonic maps , Author =. arXiv:1208.1470 [math.AP] , Year =
[215]

2008 , Pages =

Huang, Yingyan and Ma, Jing and Chang, Seongsik and Zhao, Qian and Ho, Seng-Tiong , Booktitle =. 2008 , Pages =

2008
[216]

Huybrechts, Daniel , Year =
[217]

, Publisher =

Huybrechts, D. , Publisher =. 2006 , Address =. doi:10.1093/acprof:oso/9780199296866.001.0001 , ISBN =

2006 doi
[218]

2010 , Edition =

The geometry of moduli spaces of sheaves , Author =. 2010 , Edition =

2010
[219]

1997 , Address =

The geometry of moduli spaces of sheaves , Author =. 1997 , Address =

1997
[220]

Ihl, Matthias and Kahle, Alexander , Year =
[221]

, Journal =

Ito, Y. , Journal =. Crepant resolution of trihedral singularities and the orbifold. 1995 , Number =. doi:10.1142/S0129167X95000043 , Fjournal =

1995 doi
[222]

and Nakajima, H

Ito, Y. and Nakajima, H. , Journal =. Mc. 2000 , Number =. doi:10.1016/S0040-9383(99)00003-8 , File =

2000 doi
[223]

and Reid, M

Ito, Y. and Reid, M. , Booktitle =. The. 1996 , Address =

1996
[224]

Instantons on Special Holonomy Manifolds , Author =. Phys. Rev. D , Year =
[225]

Jacob, A. and S. Mathematical Research Letters , year =
[226]

and Walpuski, T

Jacob, A. and Walpuski, T. , journal =. 2018 , number =. arXiv:1603.07702v1 [math.DG] , groups =

2018
[227]

1980 , Address =

Vortices and monopoles , Author =. 1980 , Address =

1980
[228]

2006 , Editor =

Jaffe, Arthur and Witten, Edward , Booktitle =. 2006 , Editor =

2006
[229]

Stable bundles on 3-fold hypersurfaces , Author =. Bull. Braz. Math. Soc. , Year =
[230]

Instanton sheaves on complex projective spaces , Author =. Collect. Math. , Year =
[231]

Bulletin of the London Mathematical Society , Year =

Holomorphic bundles for higher dimensional gauge theory , Author =. Bulletin of the London Mathematical Society , Year =
[232]

On the semistability of instanton sheaves over certain projective varietie , Author =. Comm. Algebra , Year =
[233]

Jardim, M. and S. 2011 , Eprint =

2011
[234]

2013 , pages =

Jiang, Yi , title =. 2013 , pages =. arXiv , arxivid =:1302.0923 , file =

2013
[235]

Joyce, D. D. , Year =
[236]

Joyce, D. D. , Note =. 2012 , Owner =

2012
[237]

2007 , Series =

Riemannian holonomy groups and calibrated geometry , Author =. 2007 , Series =

2007
[238]

, Journal =

Joyce, Dominic D. , Journal =. 2006 , Pages =. doi:10.1007/s13398-014-0173-7.2 , Eprint =

2006 doi
[239]

Joyce, D. D. , Journal =. Special. 2003 , Number =

2003
[240]

Joyce, D. D. , Booktitle =. On counting special. 2002 , Address =. doi:10.1090/conm/314/05427 , Mrclass =

2002 doi
[241]

2000 , Address =

Compact manifolds with special holonomy , Author =. 2000 , Address =

2000
[242]

Joyce, D. D. , Journal =. A new construction of compact 8--manifolds with holonomy. 1999 , Number =

1999
[243]

Joyce, D. D. , title =. 1999 , eprint =

1999
[244]

Joyce, D. D. , Journal =. Compact. 1996 , Number =

1996
[245]

Joyce, D. D. , Journal =. Compact. 1996 , Number =. doi:10.1007/s002220050039 , Fjournal =

1996 doi
[246]

Joyce, D. D. , journal =. Compact. 1996 , pages =

1996
[247]

1996 , Number =

Joyce, Dominic D , Journal =. 1996 , Number =

1996
[248]

July, Sylvie Paycha , Year =
[249]

Kac, Victor G , Year =
[250]

and Vasserot, E

Kapranov, M. and Vasserot, E. , Journal =. Kleinian singularities, derived categories and. 2000 , Number =. doi:10.1007/s002080050344 , File =

2000 doi
[251]

, Journal =

Karigiannis, S. , Journal =. Desingularization of. 2009 , Number =. doi:10.2140/gt.2009.13.1583 , Fjournal =

2009 doi
[252]

, Journal =

Karigiannis, S. , Journal =. Flows of. 2007 , Number =

2007
[253]

doi:10.1093/qmath/han020 , Eprint =

Karigiannis, Spiro , Year =. doi:10.1093/qmath/han020 , Eprint =

doi
[254]

and McKay, B

Karigiannis, S. and McKay, B. and Tsui, M-P. , Journal =. 2012 , Pages =

2012
[255]

Katz, Sheldon , File =
[256]

2015 , Pages =

Kawai, Kotaro , Journal =. 2015 , Pages =

2015
[257]

arXiv , Arxivid =:1411.5840 , File =

Kawai, Kotaro , Year =. arXiv , Arxivid =:1411.5840 , File =
[258]

Kessel, T. M. , School =
[259]

2004 , month = feb, pages =

Kim, Eui Chul , title =. 2004 , month = feb, pages =. arXiv , arxivid =:0402427 , file =

2004
[260]

Moduli of representations of finite-dimensional algebras , Author =. Quart. J. Math. Oxford Ser. (2) , Year =
[261]

Kirchberg, K. D. , journal =. 2011 , issn =. doi:10.1016/j.difgeo.2011.02.004 , file =

2011 doi
[262]

Principal fibre bundles with the

Kobayashi, Shoshichi , Journal =. Principal fibre bundles with the. 1956 , Pages =

1956
[263]

and Nomizu, K

Kobayashi, S. and Nomizu, K. , publisher =. Foundations of Differential Geometry , year =
[264]

1969 , Volume =

Foundations of Differential Geometry , Author =. 1969 , Volume =

1969
[265]

2005 , Abstract =

Koll. 2005 , Abstract =. arXiv , Arxivid =:0508332 , File =

2005
[266]

Kordyukov, Yu. A. , Journal =. 1991 , Number =

1991
[267]

Kovalev, Alexei , File =
[268]

, Year =

Kovalev, A. , Year =
[269]

Kovalev, Alexei , Year =
[270]

, journal =

Kovalev, A. , journal =. From. 2004 , pages =

2004
[271]

, Journal =

Kovalev, A. , Journal =. Twisted connected sums and special. 2003 , Pages =. doi:10.1515/crll.2003.097 , Fjournal =

2003 doi
[272]

Strings and Geometry , Publisher =

From Fano threefolds to compact _2- manifolds , Author =. Strings and Geometry , Publisher =. 2003 , Address =

2003
[273]

, title =

Kovalev, A. , title =. 2003 , eprint =

2003
[274]

and Lee, N

Kovalev, A. and Lee, N. H. , title =. 2000 , eprint =

2000
[276]

2011 , Month = jun, Number =

Kovalev, Alexei and Lee, Nam-Hoon , Journal =. 2011 , Month = jun, Number =. doi:10.1017/S030500411100003X , File =

2011 doi
[278]

and Nordstr

Kovalev, A. and Nordstr. Asymptotically cylindrical 7 --manifolds of holonomy. Ann. Global Anal. Geom. , Year =. doi:10.1007/s10455-010-9210-8 , Fjournal =

doi
[279]

K3 surfaces with non-symplectic involution and compact irreducible G_2 -manifolds , Year =

Nam-Hoon , Author =. K3 surfaces with non-symplectic involution and compact irreducible G_2 -manifolds , Year =
[280]

Kronheimer, P. B. , Journal =. Instanton invariants and flat connections on the. 1991 , Number =. doi:10.1215/S0012-7094-91-06411-2 , Fjournal =

1991 doi
[281]

Instantons and the geometry of the nilpotent variety , Author =. J. Differential Geom. , Year =
[282]

Kronheimer, P. B. , Journal =. The construction of. 1989 , Number =

1989
[283]

Kronheimer, P. B. , Journal =. A. 1989 , Number =

1989
[284]

Kronheimer, P. B. and Nakajima, H. , Journal =. Yang--. 1990 , Number =. doi:10.1007/BF01444534 , Fjournal =

1990 doi
[285]

Kuleshov, S. A. , Journal =. Stable bundles on a. 1990 , Number =

1990
[286]

2007 , month = jun, pages =

Kumar, Alok and Mukhopadhyay, Subir and Ray, Koushik , title =. 2007 , month = jun, pages =. doi:10.1088/1126-6708/2007/12/032 , eprint =

2007 doi
[287]

2006 , month = may, pages =

Kumar, Alok and Mukhopadhyay, Subir and Ray, Koushik , title =. 2006 , month = may, pages =. arXiv , arxivid =:0605083 , file =

2006
[288]

L. The. 1995 , groups =

1995
[289]

Rendiconti del Seminario Matematico di Torino , Year =

Geometric flows and their solitons on homogeneous spaces , Author =. Rendiconti del Seminario Matematico di Torino , Year =
[290]

1971 , Number =

Lawson, Blaine , Journal =. 1971 , Number =

1971
[291]

Lee, D. A. , Journal =. Connected sums of special. 2004 , Number =

2004
[292]

2002 , month = feb, number =

Lee, Jae-Hyouk and Leung, Naichung Conan , title =. 2002 , month = feb, number =. arXiv , arxivid =:0202045 , file =

2002
[293]

2006 , Number =

Leonhardt, Ulf , Journal =. 2006 , Number =. doi:10.1126/science.1126493 , Owner =

2006 doi
[294]

, school =

Lewis, C. , school =. 1999 , groups =

1999
[295]

2008 , Number =

Li, Jensen and Pendry, J B , Journal =. 2008 , Number =. doi:10.1103/PhysRevLett.101.203901 , Owner =

2008 doi
[296]

Physics Reports , Year =

The Physics and Mathematics of the Second Law of Thermodynamics , Author =. Physics Reports , Year =
[297]

and Yngvason, Jakob , Year =

Lieb, Elliott H. and Yngvason, Jakob , Year =
[298]

Lima, Elon Lages , File =
[299]

and Wang, C

Lin, F. and Wang, C. , publisher =. The analysis of harmonic maps and their heat flows , year =
[300]

Gradient estimates and blow-up analysis for stationary harmonic maps , Author =. Ann. of Math. (2) , Year =. doi:10.2307/121073 , Fjournal =

doi

Pith tools

Reviewed May 9, 2026 · model on record in the stance chip above.

[1] [1]

A falsificação nas contas oficiais da Reforma da Previdência: o caso do Regime Geral de Previdência Social , Author=

work page

[2] [2]

O mito do custo fiscal e da regressividade da aposentadoria por tempo de contribuição , Author=

work page

[3] [3]

A Contabilidade Criativa na Reforma da Previdência e o Aumento da Pobreza: Novos Dados e Tréplica à Resposta Oficial , Author=

work page

[4] [4]

The Weitzenbock formula for the Fueter

Andr. The Weitzenbock formula for the Fueter. 2022 , publisher =. doi:10.4310/cag.2022.v30.n1.a3 , url =

work page doi:10.4310/cag.2022.v30.n1.a3 2022

[5] [5]

1989 , month = mar, publisher =

Yunmei Chen and Michael Struwe , title =. 1989 , month = mar, publisher =. doi:10.1007/bf01161997 , url =

work page doi:10.1007/bf01161997 1989

[6] [6]

Journal of Differential Geometry , number =

Michael Struwe , title =. Journal of Differential Geometry , number =. 1988 , doi =

work page 1988

[7] [7]

2023 , eprint=

Flows of geometric structures , author=. 2023 , eprint=

work page 2023

[8] [8]

Sá Earp , year=

Udhav Fowdar and Henrique N. Sá Earp , year=. Harmonic flow of quaternion-. 2301.12494 , archivePrefix=

work page arXiv