Automorphisms of punctual Hilbert schemes and symmetric powers of varieties

Ashima Bansal; Shivam Vats; Supravat Sarkar

REVIEW 4 major objections 6 minor 2 cited by

Automorphisms of punctual Hilbert schemes and symmetric powers of varieties

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Pith's one-line read This paper classifies exactly when the Hilbert scheme of points on a surface has an automorphism not induced by the surface, finding four exceptional cases.

desk verdict Real completion of the BOR20 classification for surfaces, but the Hilbert-to-symmetric reduction has a genuine gap at Theorem 3.2 and leans on unpublished preprints. read the letter →

arxiv 2508.18059 v1 pith:AL2WPPFV submitted 2025-08-25 math.AG

Ashima Bansal , Supravat Sarkar , Shivam Vats This is my paper · ORCID

classification math.AG MSC 14J5014C05

keywords punctualHilbertschemesymmetricpowerautomorphismgroupbigdiagonalabeliansurfacesIitakafibrationsmoothprojectivenon-naturalautomorphisms

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 sets out to classify, for complex smooth projective surfaces, exactly when the punctual Hilbert scheme $\mathrm{Hilb}^m(X)$ admits an automorphism that is not induced by an automorphism of $X$ but preserves the big diagonal, the locus of non-reduced subschemes. It claims a complete answer: such an automorphism exists precisely in four situations: $m=2$ and $X$ is a product of curves; $X$ is an abelian surface isogenous to the square of an elliptic curve; $X$ is a simple abelian surface whose rational endomorphism algebra is neither $\mathbb{Q}$ nor an imaginary quadratic field; or $X$ belongs to a specified class of elliptic fibrations with a non-constant map from the base to the fibre. The proof reduces the Hilbert-scheme question to the analogous question for symmetric powers $S^mX$, proves the reduction is an equivalence in the relevant cases, and completes the symmetric-power classification for surfaces. If correct, this closes the classification question raised in [BOR20] and shows that non-natural symmetries are rare and explicitly listable.

What carries the argument

The load-bearing machinery is the Hilbert-Chow morphism $\mathrm{Hilb}^m(X)\to S^mX$, whose exceptional divisor is the big diagonal, paired with a descent-lift equivalence between automorphisms of the Hilbert scheme preserving the big diagonal and automorphisms of the symmetric power. The descent side is carried by a sequence of incidence strata $E_\pi$: the singular locus of the exceptional divisor forces preservation of successively smaller diagonals until the small diagonal is fixed, and the fibre over the small diagonal has Picard rank one, so curves contracted by Hilbert-Chow are contracted by any such automorphism. The lift side uses the identification of $H$ minus a codimension-two locus with a blow-up of $S^mX$ along its singular locus, together with an extension lemma for isomorphisms of complements of codimension at least two. On the symmetric-power side, the classification is driven by group-theoretic analysis of the normalizer of the symmetric group inside $\operatorname{Aut}(X^m)$; for $m=2$ the extra swap-within-blocks automorphisms form a group $(\mathbb{Z}/2\mathbb{Z})^{k-1}$, and for abelian surfaces the existence of endomorphisms $\alpha\neq\pm 1$ with $m\mid (1-\alpha)$ in $\mathrm{End}(X)$ yields explicit non-natural automorphisms.

What would settle it

Find a smooth projective surface $X$ satisfying none of the four conditions of Theorem D and an integer $m\ge 2$ for which $S^mX$ has a non-natural automorphism; this would directly contradict the claimed classification. More locally, for $X$ a surface with $m=3$, set $W=\operatorname{Sing}(S^3X)$ and $W_1=\operatorname{Sing}(W)$, then check whether the automorphism of $H\setminus E_1$ obtained from the blow-up description extends over $E_1$ by testing whether the two ample line bundles $p^*L\otimes\mathcal{O}(\alpha E)$ and $p^*\phi^*L\otimes\mathcal{O}(\alpha E)$ agree as sheaves near $E_1$; a mismatch for any surface would break Theorem B.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is a complete four-part classification. For a smooth projective surface $X$ and integer $m\ge 2$, the Hilbert scheme $\mathrm{Hilb}^m(X)$ has an automorphism preserving the big diagonal that is not induced by $\operatorname{Aut}(X)$ if and only if: (a) $m=2$ and $X$ is a product of two curves; (b) $X$ is an abelian surface isogenous to $E\times E$ for an elliptic curve $E$; (c) $X$ is a simple abelian surface with $\mathrm{End}_{\mathbb{Q}}(X)$ neither $\mathbb{Q}$ nor an imaginary quadratic extension of $\mathbb{Q}$; or (d) $X$ lies in class $C$, meaning $X=(D\times Y)/G$ with $D$ elliptic, $Y$ of general type, and $G$ a finite subgroup of $\operatorname{Aut}^0(D)$ acting diagonally, and the base of the Iitaka fibration maps non-constantly to the fibre. The paper further claims that the same four conditions characterize non-natural automorphisms of $S^mX$ for surfaces, and that for higher-dimensional varieties with $H^1(X,\mathcal{O}_X)=0$ or $K_X$ ample, every big-diagonal-preserving automorphism of $\mathrm{Hilb}^mX$ for $m=2,3$ is natural. The bridge is Theorem B: for $n=2$ or $m\le 3$, the Hilbert scheme has a non-natural big-diagonal-preserving automorphism if and only if the symmetric power does.

Load-bearing premise

The load-bearing premise is that every automorphism of the symmetric power $S^mX$ lifts to an automorphism of the punctual Hilbert scheme that preserves the big diagonal; the paper's proof of this lift is a sketch that does not fully verify that the isomorphism extends across the locus where the blow-up identification is not literally valid. If that extension fails, the equivalence between Hilbert-scheme automorphisms and symmetric-power automorphisms collapses.

Editorial extensions

If this is right

For surfaces of Kodaira dimension at least one, $\mathrm{Hilb}^m(X)$ has a non-natural automorphism without any big-diagonal assumption exactly in cases (a) and (d) of Theorem A.
For higher-dimensional varieties with $H^1(X,\mathcal{O}_X)=0$ or ample canonical bundle, $\mathrm{Hilb}^2(X)$ and $\mathrm{Hilb}^3(X)$ admit no non-natural automorphism preserving the big diagonal when $X$ is indecomposable in the $m=2$ case.
The pair consisting of $\mathrm{Hilb}^mX$ together with its big diagonal determines $X$ up to isomorphism in the cases covered by Theorem B.
For surfaces of Kodaira dimension at least one, the punctual Hilbert scheme $\mathrm{Hilb}^mX$ alone determines $X$ up to isomorphism.
The classification of non-natural automorphisms of symmetric powers of smooth projective surfaces is now complete and matches the Hilbert-scheme classification.

Reading between the lines

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

The reduction suggests a testable principle for higher dimensions: whenever the relevant Hilbert-Chow fibre has Picard rank one and the exceptional strata form a good stratification, big-diagonal-preserving automorphisms should descend to symmetric powers beyond $m\le 3$; the current bottleneck is the lift step, whose sketch may require a full blow-up argument.
The class-$C$ examples show that non-natural automorphisms can arise from variation in the fibres of an isotrivial fibration rather than from endomorphism rings of abelian varieties; the same mechanism could plausibly produce exotic automorphisms of symmetric powers of higher-dimensional fibrations.
For abelian varieties of dimension at least two, the paper's remark identifying the kernel of $\operatorname{Aut}(S^mX)\to\operatorname{Aut}(X)$ with a congruence subgroup invites an explicit computation of these kernels for other varieties with large endomorphism rings, such as products of elliptic curves.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Dear colleague, the headline: this is a real completion of the BOR20 classification, and the symmetric-power classification is new. The paper is worth a serious referee, but you should know that the reduction from Hilbert schemes to symmetric powers has a load-bearing sketch at Theorem 3.2, and the paper leans on two unpublished companion preprints for key facts.

What is new and good: Theorem A gives the complete list of surfaces whose punctual Hilbert scheme has a non-natural automorphism preserving the big diagonal: product of curves with m=2, abelian surfaces isogenous to a square of an elliptic curve, simple abelian surfaces with End_Q not Q or imaginary quadratic, and class C surfaces with a non-constant map from base to fibre of the Iitaka fibration. That answers Question 1 of BOR20 and unifies scattered partial results. Theorem D does the same for symmetric powers, which is the right analogue in higher dimension. Theorem C gives useful sufficient conditions in higher dimension. The group-theoretic normalizer computation in Section 4 is careful and convincing. Lemma 3.4, on automorphisms of projective bundles not over the base, is a nice standalone result.

The soft spots are real. Theorem 3.2 is the bridge: it claims any automorphism of S^mX lifts to Hilb^mX. The proof is a sketch. It invokes Cha79 and BK05 to identify H\E1 -> S^mX\W1 as the blow-up of S^mX\W1 along W\W1, but does not check the cases needed (m>=3 with n>=3 and m>=4 with n=2), does not check that the exceptional divisor is the projectivized normal bundle with the right O(-1), and the extension argument via Lemma 3.15 is compressed. The line 'Since phi^{-1}(E\E1)=E\E1' needs E\E1 invariant as a scheme, not just as a set, and the codimension of W1 verified. None of that is in the text. If that lift fails, Theorem B collapses, and the Hilbert-scheme classification would not follow from Theorem D. That is a genuine gap, not a nitpick.

Also, several load-bearing facts are imported from the authors' own unpublished preprints [BSV25a] and [BSV25b]: the normalization of W(3) is X×X, Lemma 2.6 on multiprojective bundles, Corollary 4.2 on symmetric powers determining the variety. The authors are transparent about this, but it does mean the derivation is not self-contained. The reliance is heavy enough that a referee cannot fully verify the paper without those preprints.

The classification itself may well be right. The descent direction (Theorem 3.1) looks solid, and the surface analysis in Section 5 is systematic. This deserves peer review, not desk rejection. I would ask the authors in revision to expand Theorem 3.2 into a full proof, and to either fold the preprint results into the paper or make them available in complete form. If those two things are addressed, I would take the classification. For a reading group, I would hold off until the companion preprints are out.

Referee Report

4 major / 6 minor

Summary. The paper classifies, for smooth complex projective surfaces X and integers m≥2, the pairs (m,X) for which the punctual Hilbert scheme Hilb^m(X) admits a non-natural automorphism preserving the big diagonal (Theorem A). The classification has four cases: m=2 with X a product of curves; X an abelian surface isogenous to the square of an elliptic curve; X a simple abelian surface with End_Q(X) not Q and not an imaginary quadratic extension; and X in a class C of isotrivial elliptic surfaces with a non-constant map from the base to a fibre of the Iitaka fibration. The proof reduces the Hilbert-scheme problem to an analogous problem for symmetric powers S^m X (Theorem B), then classifies non-natural automorphisms of symmetric powers of surfaces (Theorem D), with a sufficient criterion in higher dimensions (Theorem C). A corollary treats surfaces of Kodaira dimension at least 1 without the diagonal-preserving hypothesis (Corollary A).

Significance. If correct, Theorem A completely answers Question 1 of Belmans-Oberdieck-Rennemo and provides a full classification of non-natural automorphisms of symmetric powers of surfaces. The reduction Theorem B is a valuable structural bridge between Hilbert schemes and symmetric powers, and Theorem C(i) gives a clean description of Aut(S^2 X) under rigidity hypotheses. The paper contains explicit new examples (the class C surfaces) and the classification statements are precise and falsifiable. The group-theoretic lemmas in Section 4 are well executed. However, the proof of the lift direction Theorem 3.2 is only a sketch with a key step that is not justified, and the descent proof in Theorem 3.1 has notational inconsistencies that obscure the main stratification argument; both are load-bearing for the central result. The paper also depends on two unpublished same-author preprints for structurally important facts.

major comments (4)

[§3, proof of Theorem 3.2] The proof of the lift direction is not complete. After constructing an automorphism φ1 of U=H\E1 over the base automorphism φ of S^mX\W1, the text invokes Lemma 3.15 to extend φ1 to H. Lemma 3.15 requires an equality φ1^*(M|_V)=L|_U of line bundles on U, but the only stated justification is 'Since φ1^{-1}(E\E1)=E\E1'. This does not provide the required equality: because φ1 covers φ on the base, φ1^*p^*L = p^*φ^*L, not p^*L, and the two line bundles p^*L⊗O(αE) and p^*φ^*L⊗O(αE) are not shown to agree on U; ρ(U)=1 gives only proportionality, not equality. Moreover, the identification of H\E1 as the blow-up of S^mX\W1 along W\W1 via [Cha79] and [BK05, Exercise 7.3E(5)] is asserted without verifying the needed cases (n=2 with m≥4, and n=3 with m=3). Please supply a complete proof of Theorem 3.2, including a precise verification of the extension criterion.
[§3, Lemmas 3.11-3.12 and Theorem 3.1, Case 3] The stratification argument in Case 3 uses the notation E_{(t,1)}, E_{(t-1,2,1)}, E_{(2,2,1)}, etc., which is undefined for the stated m because Section 2 defines E_{π,m} only for partitions π of m. For instance, (2,2,1) is not a partition of 4. The intended meaning is clearly the partition with additional trailing 1's, but this shorthand is never introduced, making Lemmas 3.11 and 3.12 as written ill-formed for general m. The induction step 'F_t = E_{(t,1)} for all 3≤t≤m-1' is also inconsistent with F_3 having two components when m=4. Please rewrite the stratification with explicit partitions of m and give a rigorous induction from F_3 to F_m.
[§4, proof of Theorem C(i)] The proof lifts an arbitrary automorphism ψ of S^mX to an automorphism φ of X^m by citing [BOR20, Proposition 9 and 12] and asserting that the proof is valid for every smooth projective variety X. Since [BOR20] is stated for surfaces and the branch locus of X^m→S^mX has codimension at least 2 when dim X ≥ 3, the lift is not a formal consequence of the surface argument. This step is load-bearing for Theorem C(i) and hence for Theorem A(2). Please provide a self-contained proof of the lift in the generality used, or restate the required theorem explicitly.
[§3 and §5, reliance on [BSV25a] and [BSV25b]] The paper relies for structurally important facts on two unpublished same-author preprints: [BSV25b, Theorem 2] is used in the proof of Theorem 3.1 (normalization of W and dimension of W_{(m)}), and [BSV25a, Lemma 2.6 and Corollary 4.2] are used in Theorem C(ii) and Remark 3.14. These results are not stated in the manuscript. Please either include the statements, and ideally proofs, of the needed results, or confirm that the preprints are in final accepted form and give precise statements that the reader can verify independently.

minor comments (6)

[§3, Lemma 3.9] The statement 'ρ(Hilb^m X \ S^m(X)) = 1' is not meaningful as written, since S^m(X) is not a subset of Hilb^m X; the intended open set is presumably the complement of the exceptional divisor E of the Hilbert-Chow morphism.
[§2 and §3] Please introduce explicitly the convention that E_{(a_1,...,a_k)} stands for the stratum associated to the partition of m obtained by adding (m - Σ a_i) ones; this shorthand is used in Lemmas 3.11-3.12 and Theorem 3.1 without definition.
[§5, Theorem 5.6] The proof of Theorem 5.6 invokes Lemma 5.5, which assumes X is not an abelian surface, but the theorem statement does not include this hypothesis; either add the hypothesis or handle abelian surfaces separately in the proof.
[§5, Lemma 5.2] There is a grammatical typo in the statement: 'LetX is an abelian surface' should be 'Let X be an abelian surface'; similar minor typos occur in Lemma 5.9 and elsewhere.
[§3, Theorem 3.1 Case 2] The reduction of the fibre of Hilb^3X→S^3X over w∈W_{(3)} to the local model H_{3,n} of Lemma 3.7 is not stated; please clarify the local isomorphism used.
[§5, Theorem 5.6 Step 1] The claim that p^{(m)} is the contraction part of the Albanese map of X^m when p is the contraction part of the Albanese map of X is stated without proof; a brief justification would help the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the Hilbert-to-symmetric reduction and surface classification do not assume their conclusions.

full rationale

Theorem A is not obtained by assuming Theorem A. It is assembled from Theorems B, C(i), and D. Theorem D is a standalone classification of non-natural automorphisms of symmetric powers whose converse is proved from the Enriques–Kodaira classification, [BOR20]'s lifting result, Lemmas 5.1–5.8, and [Fon24]; none of these inputs contains the Hilbert-scheme conclusion. Theorem B is a geometric equivalence proved by descent (Theorem 3.1) and lift (Theorem 3.2). Descent uses [BSV25b, Theorem 2] for the normalization of Sing(S^3X), [Cha79]/[BK05] for the blow-up structure, and [BOR20]; these are structural facts about symmetric powers and Hilbert–Chow morphisms, not restatements of the target. The same-author preprints [BSV25a], [BSV25b], and [BSV23] are invoked for lemmas on multiprojective bundles and symmetric-power singular loci; they are parameter-free structural statements and do not assume the non-natural-automorphism classification, so under the stated rules they count as independent support rather than circularity. The lift proof in Theorem 3.2 is compressed and leaves the extension across exceptional loci under-verified; that is a rigor gap, not a circular reduction. No fitted parameter is renamed as a prediction, and no equation in the paper is equivalent to its input by construction. Therefore the circularity score is 0.

Assumptions & free parameters 0 free parameters · 10 assumptions · 0 invented entities

No free parameters or invented entities. The proof stack is a long chain of external structure theorems; the heaviest burden is the three citations to the authors' own unpublished companion preprints [BSV25a, BSV25b] for normalization and multiprojective-bundle facts, plus the sketched blow-up lifting in Theorem 3.2.

assumptions (10)

standard math Fogarty: Hilb^m(X) is smooth and irreducible for smooth projective surfaces.
Basis for considering automorphisms of Hilb^m(X) for surfaces; cited to [Fog68].
standard math Skjelnes-Smith: for dimension at least 3, Hilb^m(X) is smooth only for m at most 3.
Limits Theorem B to m at most 3 in higher dimension; cited to [SS20].
domain assumption [BOR20, Propositions 9 and 12]: every automorphism of S^mX lifts to an automorphism of X^m.
Used at the start of Theorem C(i) and in Theorems 5.6, 5.7, and 5.8; published result with proof.
ad hoc to paper [BSV25b, Theorem 2]: structural description of the normalization of the relevant strata W in S^mX.
Used in the m=3 case of Theorem 3.1; same-authors unpublished preprint, statement not reproduced.
ad hoc to paper [BSV25a, Lemma 2.6]: isomorphism criterion for multiprojective bundles over Y^m.
Used in the proof of Theorem C(ii); same-authors unpublished preprint.
ad hoc to paper [BSV25a, Corollary 4.2]: S^mX determines X up to isomorphism in the relevant range.
Used in Remarks 3.14 and 5.13 to conclude that X is determined by Hilb^mX plus the big diagonal; same-authors preprint.
domain assumption [Cha79] and [BK05, Exercise 7.3E(5)]: H minus E1 is the blow-up of S^mX along W minus W1.
Key to the sketched lifting proof of Theorem 3.2.
domain assumption [Fon24, Theorem D]: structure of class C surfaces and their connected automorphism groups.
Used in Lemma 5.5 and Theorem D to establish and exclude case (4).
domain assumption [Mae79, Theorem 2]: for a non-isotrivial fibration, very general fibres admit no non-constant maps from X^{m-1}.
Used in Theorem 5.7 to force component automorphisms to be identity.
domain assumption [GV94, Appendix]: End(X)^times is infinite for abelian surfaces with indefinite quaternion endomorphism algebra.
Used in case (3) of Theorem D to produce non-natural automorphisms.

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Pith. "Pith review of Automorphisms of punctual Hilbert schemes and symmetric powers of varieties." pith.science (2026). https://pith.science/paper/AL2WPPFV

@misc{pith2026250818059,
  author       = {Pith},
  title        = {Pith review of: Automorphisms of punctual Hilbert schemes and symmetric powers of varieties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AL2WPPFV}},
  note         = {Machine review of arXiv:2508.18059}
}

abstract

We classify complex smooth projective surfaces whose punctual Hilbert scheme has a non-natural automorphism preserving the big diagonal. This completely answers a question raised by Belmans, Oberdieck and Rennemo, and extends previous works by Boissi{\`e}re-Sarti, Hayashi, Sasaki, Girardet and Wang. We reduce this to studying the existence of non-natural automorphisms of symmetric powers. We study this question for higher dimensional varieties too, giving some sufficient conditions guaranteeing every automorphism of a symmetric power to be natural. As a corollary, we characterize smooth projective surfaces of Kodaira dimension $\geq 1$ whose punctual Hilbert scheme has a non-natural automorphism, this time not assuming the automorphism preserves the big diagonal. We also address the question, when a smooth projective variety is determined up to isomorphism by its punctual Hilbert scheme.

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Cited by 2 Pith papers

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Works this paper leans on

5 extracted references · 4 canonical work pages · cited by 2 Pith papers

[1]

Nonisolated Saito singularities

[Ale90] Alexandr G Aleksandrov. “Nonisolated Saito singularities”. In: Mathematics of the USSR-Sbornik65.2 (1990), p

work page 1990
[5]

Automorphisms of symmetric powers and motivic zeta functions

Tata Institute of Fundamental Re- search Studies in Mathematics. With appendices by C. P. Ramanujam and Yuri Manin, Corrected reprint of the second (1974) edition. Tata Institute of Fundamental Research, Bombay; by Hindustan Book Agency, New Delhi, 2008, pp. xii+263.isbn: 978-81-85931-86-9; 81-85931-86-0. [Occ+23] Gianluca Occhetta et al. “Small bandwidth...

work page Pith review arXiv 1974
[80]

Automorphisms of Hilbert Schemes of Points on Abelian Surfaces

Fields Inst. Commun. Fields Inst. Res. Math. Sci., Toronto, ON, 2017, pp. 321–352. [Fog68] John Fogarty. “Algebraic families on an algebraic surface”. In:American Jour- nal of Mathematics90.2 (1968), pp. 511–521. [Fon24] Pascal Fon. “Connected algebraic groups acting on algebraic surfaces”. In: Ann. Inst. Fourier (Grenoble)74.2 (2024), pp. 545–587. [Gir24...

work page Pith review arXiv 1968
[231]

Automorphisms of Hilbert schemes of points on surfaces

Progress in Mathematics. Birkhäuser Boston, Inc., Boston, MA, 2005, pp. x+250. [BOR20] Pieter Belmans, Georg Oberdieck, and Jørgen Rennemo. “Automorphisms of Hilbert schemes of points on surfaces”. In:Transactions of the American Math- ematical Society373.9 (2020), pp. 6139–6156. [BS12] Samuel Boissière and Alessandra Sarti. “A note on automorphisms and b...

arXiv 2020
[561]

Description de HilbnC{x,y}

[Bc77] Joël Brian¸con. “Description de HilbnC{x,y}”. In:Invent. Math.41.1 (1977), pp. 45–89. [Bea83] Arnaud Beauville. “Some remarks on Kahler manifolds with c_1= 0”. In: Classification of algebraic and analytic manifolds, Katata, 1982(1983). [BEB09] Ragnar-OlafBuchweitz,WolfgangEbeling,andHans-ChristianGrafvonBoth- mer. “Low-dimensional singularities wit...

work page 1977

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Nonisolated Saito singularities

[Ale90] Alexandr G Aleksandrov. “Nonisolated Saito singularities”. In: Mathematics of the USSR-Sbornik65.2 (1990), p

work page 1990

[2] [5]

Automorphisms of symmetric powers and motivic zeta functions

Tata Institute of Fundamental Re- search Studies in Mathematics. With appendices by C. P. Ramanujam and Yuri Manin, Corrected reprint of the second (1974) edition. Tata Institute of Fundamental Research, Bombay; by Hindustan Book Agency, New Delhi, 2008, pp. xii+263.isbn: 978-81-85931-86-9; 81-85931-86-0. [Occ+23] Gianluca Occhetta et al. “Small bandwidth...

work page Pith review arXiv 1974

[3] [80]

Automorphisms of Hilbert Schemes of Points on Abelian Surfaces

Fields Inst. Commun. Fields Inst. Res. Math. Sci., Toronto, ON, 2017, pp. 321–352. [Fog68] John Fogarty. “Algebraic families on an algebraic surface”. In:American Jour- nal of Mathematics90.2 (1968), pp. 511–521. [Fon24] Pascal Fon. “Connected algebraic groups acting on algebraic surfaces”. In: Ann. Inst. Fourier (Grenoble)74.2 (2024), pp. 545–587. [Gir24...

work page Pith review arXiv 1968

[4] [231]

Automorphisms of Hilbert schemes of points on surfaces

Progress in Mathematics. Birkhäuser Boston, Inc., Boston, MA, 2005, pp. x+250. [BOR20] Pieter Belmans, Georg Oberdieck, and Jørgen Rennemo. “Automorphisms of Hilbert schemes of points on surfaces”. In:Transactions of the American Math- ematical Society373.9 (2020), pp. 6139–6156. [BS12] Samuel Boissière and Alessandra Sarti. “A note on automorphisms and b...

arXiv 2020

[5] [561]

Description de HilbnC{x,y}

[Bc77] Joël Brian¸con. “Description de HilbnC{x,y}”. In:Invent. Math.41.1 (1977), pp. 45–89. [Bea83] Arnaud Beauville. “Some remarks on Kahler manifolds with c_1= 0”. In: Classification of algebraic and analytic manifolds, Katata, 1982(1983). [BEB09] Ragnar-OlafBuchweitz,WolfgangEbeling,andHans-ChristianGrafvonBoth- mer. “Low-dimensional singularities wit...

work page 1977