Defines virtual cycles for 3-term complexes via blow-up modifications of the complex and applies them to Hilbert schemes of surfaces to strengthen known results on reduced and virtual cycles.
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12 Pith papers cite this work, alongside 994 external citations. Polarity classification is still indexing.
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Proves Eff^k(ar M_{g,n}) has infinitely many extremal rays for k≥2, g≥3, n≥2k-2; is non-polyhedral for k≥2, g≥1, n≥k+5; and every rational tails boundary stratum is extremal, via refined use of nef kappa divisors.
Khovanskii's Bézout-type bound for Pfaffian systems is asymptotically sharp in chain-degree α (via α^s zeros) and in degrees β (via Ω(β^{n+s}) zeros).
The authors build a resolution stack for the KSBA-K-moduli wall crossing of plane quartics and compute its Chow ring and cohomology with rational coefficients.
The perturbative c=1 string S-matrix equals a double-scaled matrix integral on the spectral curve x=2√2 cos(z), y=sin(z), establishing a worldsheet–MQM–matrix-integral triality.
Oriented cohomology rings of semisimple groups admit finite presentations via formal Demazure operators; explicit minimal presentations are given for adjoint and simply-connected groups of types A1, A2, B2.
CR Paneitz operator on non-embeddable 3D tori has infinitely many negative eigenvalues under mild assumptions.
K-theory rings of toric and flag varieties are realized as quotients of group algebras from linear families of virtual polytopes, yielding natural relations and descriptions of structure sheaf classes, including in the T-equivariant case.
Matrix representations for implicitization of rational hypersurfaces via syzygies on coefficient ideals in the Cox ring, removing the LCI-at-base-points requirement for surfaces.
Generalizes positivity theorems of Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles to smooth proper DM stacks admitting projective coarse moduli spaces.
Positivity of rank-g Picard bundles on g-fold symmetric products implies degree of irrationality bounds of 2^g for genus g Jacobians and 2^{2g-3} for (g-1)-dimensional Pryms.
citing papers explorer
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Virtual cycles of 3-term complexes and the Hilbert schemes of surfaces
Defines virtual cycles for 3-term complexes via blow-up modifications of the complex and applies them to Hilbert schemes of surfaces to strengthen known results on reduced and virtual cycles.
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Extremal Effective Cycles and Nef Line Bundles on \(\overline{\rm{M}}_{g,n}\)
Proves Eff^k(ar M_{g,n}) has infinitely many extremal rays for k≥2, g≥3, n≥2k-2; is non-polyhedral for k≥2, g≥1, n≥k+5; and every rational tails boundary stratum is extremal, via refined use of nef kappa divisors.
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Parameterwise Sharpness of Khovanskii's Bezout-type Bound for Pfaffian Functions
Khovanskii's Bézout-type bound for Pfaffian systems is asymptotically sharp in chain-degree α (via α^s zeros) and in degrees β (via Ω(β^{n+s}) zeros).
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Chow and cohomology rings of moduli stacks of plane quartics
The authors build a resolution stack for the KSBA-K-moduli wall crossing of plane quartics and compute its Chow ring and cohomology with rational coefficients.
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$c=1$ strings as a matrix integral
The perturbative c=1 string S-matrix equals a double-scaled matrix integral on the spectral curve x=2√2 cos(z), y=sin(z), establishing a worldsheet–MQM–matrix-integral triality.
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A technique for computing oriented cohomology rings of semisimple algebraic groups
Oriented cohomology rings of semisimple groups admit finite presentations via formal Demazure operators; explicit minimal presentations are given for adjoint and simply-connected groups of types A1, A2, B2.
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Non-embeddable torus and CR Paneitz operator
CR Paneitz operator on non-embeddable 3D tori has infinitely many negative eigenvalues under mild assumptions.
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Polyhedral models for K-theory of toric and flag varieties
K-theory rings of toric and flag varieties are realized as quotients of group algebras from linear families of virtual polytopes, yielding natural relations and descriptions of structure sheaf classes, including in the T-equivariant case.
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Implicitization of rational hypersurfaces by syzygies with respect to coefficient ideals
Matrix representations for implicitization of rational hypersurfaces via syzygies on coefficient ideals in the Cox ring, removing the LCI-at-base-points requirement for surfaces.
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Positivity in the context of Hodge modules and Higgs bundles on Deligne-Mumford stacks
Generalizes positivity theorems of Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles to smooth proper DM stacks admitting projective coarse moduli spaces.
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Picard bundles and the degree of irrationality of Jacobians and Pryms
Positivity of rank-g Picard bundles on g-fold symmetric products implies degree of irrationality bounds of 2^g for genus g Jacobians and 2^{2g-3} for (g-1)-dimensional Pryms.
- The integral Chow ring of $\mathscr{M}_{0}(\mathbb{P}^r, 2)$