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Hsian-Hua Tseng

Publications and source records attributed to Hsian-Hua Tseng.

At least 19 recordsLinked to original sources
arXiv2026

Universality of $\mathsf{CohFT}$ of $\mathsf{Hilb}_n(S)$

By virtue of their relation to Fulton--MacPherson compactifications, the cohomological field theory of Hilbert schemes of points on a surface, in extremal curve classes, is universally and effectively determined by the characteristic numbers of the surface and by the corresponding theory of Hilbert schemes of the affine plane. As a consequence, we compute the extremal genus 1 Gromov--Witten invariants of Hilbert schemes of all surfaces.

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arXiv2026

Quantum cohomology, Hitchin systems, and Fourier--Mukai comparison

Let $X$ be the moduli space of stable trace-free rank $r$ Higgs bundles over a smooth projective curve $C$ with fixed determinant $Λ\in\Pic(C)$ and $\gcd(r,\degΛ)=1$. We prove that the $\cc^*$-equivariant quantum product of a divisor on $X$ is given by the Steinberg correspondence of the Lagrangian Steinberg cycle in $X\times X$. The Steinberg cycle is the image of the reduced virtual fundamental cycle of the $2$-pointed Kontsevich stable map space to $X$ under evaluation map. For $Γ=\Pic^0(C)[r]$, we give a character decomposition for $Γ$-invariant curve classes or finite orbit sums. In rank two and genus two we explicitly determine its fifteen endoscopic lines and the reduced spectral discriminant. %The resulting endoscopic support statement is cohomological, not a determination of the entire Chow cycle. For $\widehat X=[X/Γ]$, which is the moduli space of stable $\PGL_r$-Higgs bundles over $C$. We consider the orbifold quantum cohomology theory from a gerbe-twisted theory. The complex K-theory $\KU^*(X)$ and twisted K-theory $\KU^*([X/Γ],α)$ by the lifting $μ_r$-gerbe $α$ of the universal projective bundle is an isomorphism, and is given by the Fourier-Mukai transformation. We prove that the Fourier-Mukai transformation is compatible with the quantum product by the divisors.

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arXiv2026

Virasoro Constraints for Orbifold Curves

We prove the Virasoro constraints for the relative Gromov--Witten theory of all smooth projective effective orbifold curves, allowing relative conditions at ordinary points. The absolute Jiang--Tseng Virasoro conjecture for smooth projective effective orbifold curves follows as a corollary.

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arXiv2026

Virasoro Recursions for Simplicially Stable Curves with Colliding Markings

We study descendant integrals on moduli stacks of simplicially stable curves. For each finite collision complex, we factor the reduction morphism into elementary wall crossings and obtain a reconstruction formula in terms of ordinary Witten-Kontsevich correlators. We use the formula to derive corrected Virasoro recursions. We then package all finite-support theories in a completed disjoint-support Fock space, where the extended potential is a cumulant translate of the Witten-Kontsevich potential.

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arXiv2026

On the Toda hierarchy for the stationary theory of the tube with negative contact orders

We construct a master $2$-Toda tau sequence for the stationary relative theory of $(\PP^1,0,\infty)$ with any fixed finite lists of negative contacts. The negative-contact blocks are encoded by finite products of exponentials of infinite-wedge Lie algebra elements, with the block at $\infty$ taken as the adjoint of the entire corresponding left block. After adjoining independent positive-profile Toda times, the resulting charged-vacuum matrix elements form a genuine $2$-Toda tau sequence. Following the standard $Q,u$ specialization, its positive signed-degree coefficients recover the stationary relative Gromov--Witten invariants with the prescribed positive and negative contacts, which occur in and are constrained by the induced coefficientwise Hirota equations. The master tau sequence is larger than the enumerative sector: it generally contains nonzero, non-vacuum signed-degree-zero coefficients, as well as auxiliary nonzero lattice components, for which no enumerative interpretation is asserted. Consequently the Hirota equations form a coupled master system and do not, without additional input, close on the positive-degree invariants alone. The construction uses the large-root definition of negative contact, the Johnson--Kumaran--Wu operator formula for the tube, and the Kyoto/Plücker construction of the $2$-Toda hierarchy.

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arXiv2026

Higher Genus Gromov-Witten Theory of C^n/Z_n II: Crepant Resolution Correspondence

We study the structure of the higher genus Gromov-Witten theory of the total space $K\mathbb{P}^{n-1}$ of the canonical bundle of the projective space $\mathbb{P}^{n-1}$. We prove the finite generation property for the Gromov-Witten potential of $K\mathbb{P}^{n-1}$ by working out the details of its cohomological field theory (CohFT). More precisely, we prove that the Gromov-Witten potential of $K\mathbb{P}^{n-1}$ lies in an explicit polynomial ring using the Givental-Teleman classification of the semisimple CohFTs. In arXiv:2301.08389, we carried out a parallel study for $[\mathbb{C}^n/\mathbb{Z}_n]$ and proved that the Gromov-Witten potential of $[\mathbb{C}^n/\mathbb{Z}_n]$ lies in a similar polynomial ring. The main result of this paper is a crepant resolution correspondence for higher genus Gromov-Witten theories of $K\mathbb{P}^{n-1}$ and $[\mathbb{C}^n/\mathbb{Z}_n]$, which is proved by establishing an isomorphism between the polynomial rings associated to $K\mathbb{P}^{n-1}$ and $[\mathbb{C}^n/\mathbb{Z}_n]$. This paper generalizes the works of Lho-Pandharipande arXiv:1804.03168 for the case of $[\mathbb{C}^3/\mathbb{Z}_3]$ and Lho arXiv:2211.15878 for the case $[\mathbb{C}^5/\mathbb{Z}_5]$ to arbitrary $n\geq 3$.

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arXiv2026

Descendant and Fourier-Mukai equivalences for simple flops

For a simple flop $X\dashrightarrow X'$, we construct a correspondence between genus $0$ descendant Gromov-Witten theories of $X$ and $X'$. We show that the Fourier-Mukai equivalence induced by $X\dashrightarrow X'$ is compatible, in a precise sense, with the descendant correspondence.

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arXiv2025

Superconnection and Orbifold Chern character

We use flat antiholomorphic superconnections to study orbifold Chern character following the method introduced by Bismut, Shen, and Wei. We show the uniqueness of orbifold Chern character by proving a Riemann-Roch-Grothendieck theorem for orbifold embeddings.

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arXiv2025

Crepant Transformation Correspondence For Toric Stack Bundles

We prove a crepant transformation correspondence in genus zero Gromov-Witten theory for toric stack bundles related by crepant wall-crossings of the toric fibers. Specifically, we construct a symplectic transformation that identifies $I$-functions toric stack bundles suitably analytically continued using Mellin-Barnes integral approach. We compare our symplectic transformation with a Fourier-Mukai isomorphism between the $K$-groups.

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arXiv2025

Gromov-Witten theory of $\mathsf{Hilb}^n(\mathbb{C}^2)$ and Noether-Lefschetz theory of $\mathcal{A}_g$

We calculate the genus 1 Gromov-Witten theory of the Hilbert scheme $\mathsf{Hilb}^n(\mathbb{C}^2)$ of points in the plane. The fundamental 1-point invariant (with a divisor insertion) is calculated using a correspondence with the families local curve Gromov-Witten theory over the moduli space $\overline{\mathcal{M}}_{1,1}$. The answer exactly matches a parallel calculation related to the Noether-Lefschetz geometry of the moduli space $\mathcal{A}_g$ of principally polarized abelian varieties. As a consequence, we prove that the associated cycle classes satisfy a homomorphism property for the projection operator on $\mathsf{CH}^*(\mathcal{A}_g)$. The fundamental 1-point invariant determines the full genus 1 Gromov-Witten theory of $\mathsf{Hilb}^n(\mathbb{C}^2)$ modulo a nondegeneracy conjecture about the quantum cohomology. A table of calculations is given.

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arXiv2025

Simple Grassmannian flops

We introduce a class of flops between projective varieties modelled on direct sums of universal subbundles of Grassmannians. We study basic properties of these flops.

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arXiv2025

On the derived category of a toric stack bundle

We establish some properties of the derived category of torus-equivariant coherent sheaves on a split toric stack bundle. Our main result is a semi-orthogonal decomposition of such a category.

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arXiv2024

Higher Genus Gromov-Witten Theory of C^n/Z_n I: Holomorphic Anomaly Equations

We study the structure of higher genus Gromov-Witten theory of the quotient stack $[\mathbb{C}^n/\mathbb{Z}_n]$. We prove holomorphic anomaly equations for $[\mathbb{C}^n/\mathbb{Z}_n]$, generalizing previous results of Lho-Pandharipande arXiv:1804.03168 for the case of $[\mathbb{C}^3/\mathbb{Z}_3]$ and ours arXiv:2211.15878 for the case $[\mathbb{C}^5/\mathbb{Z}_5]$ to arbitrary $n\geq{3}$.

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