Shizhuo Zhang

activity

20172026

most citedCategorical Torelli theorems for Gushel-Mukai threefolds

10 citations · 33 across the 24 of their papers we have counts for

collaborators

28 papers

math.AG2026

A refinement of the strange duality conjecture on K3 surfaces

Shizhuo Zhang, Yu Zhao

Let $v, w$ be primitive Mukai vectors of positive rank on a polarized K3 surface with $χ (v \otimes w) = 0$ . Marian and Oprea conjectured that the strange duality map $H^0(M(v),Θ_w)^\ve…

math.AG2026

Orlov's rationality conjecture for surfaces

Xun Lin, Shizhuo Zhang

We prove that a smooth projective surface over $C$ admitting a full exceptional collection of line bundles is rational.

math.AG2026

Categorical Torelli theorem for (weighted) hypersurfaces via singularity category

Xun Lin, Jieheng Zeng, Shizhuo Zhang

We prove categorical Torelli theorems for ordinary and weighted hypersurfaces using the singularity category of the completed affine cone. For Fano hypersurfaces we use the Kuznets…

math.AG2026

Categorical reconstruction of del Pezzo surfaces: Hochschild--Serre algebras and spinor modifications

Xun Lin, Marco Rampazzo, Shizhuo Zhang

We prove that, for every smooth complex del Pezzo surface of degree at most four, the enhanced right orthogonal to the structure sheaf determines the surface up to isomorphism. In…

math.AG2026

A note on the noncommutative Hodge conjecture for graded matrix factorizations

Xun Lin, Shizhuo Zhang

Let $m \geq 2$ and $d \geq 7$ . We consider homogeneous polynomials in $2 m + 2$ variables of the form $f = F_{0} (u_{0}, v_{0}) + \dots + F_{m} (u_{m}, v_{m})$ , where the $F_{i}$ are independently very genera…

math.AG2026

Categorical resolutions and birational geometry of nodal Gushel-Mukai varieties

Kacper Grzelakowski, Marco Rampazzo, Shizhuo Zhang

We study ordinary Gushel--Mukai varieties with one node in dimensions three, four, and five, under some generality hypotheses. The blowup of the node is related by a relative Atiya…

math.AG2025

EPW varieties as moduli spaces on ordinary GM surfaces and special GM threefolds

Ziqi Liu, Shizhuo Zhang

We show that the double dual EPW sextic associated with a strongly smooth Gushel-Mukai surface can be realized as a moduli space of semistable objects on its bounded derived catego…

math.AG2025

Infinitesimal Torelli problems for special Gushel-Mukai and related Fano threefolds: Hodge theoretical and categorical perspectives

Xun Lin, Shizhuo Zhang, Zheng Zhang

A hyperelliptic curve is the classical example of a variety for which the global Torelli theorem holds while the differential of the period map has a kernel, forced by the extra in…

math.AG2025

Double EPW cubes from twisted cubics on Gushel-Mukai fourfolds

Soheyla Feyzbakhsh, Hanfei Guo, Zhiyu Liu +1

In this paper, we conduct the first systematic investigation of twisted cubics on Gushel-Mukai (GM) fourfolds. We then study the double EPW cube, a 6-dimensional hyperkähler manifo…

math.AG2024★ 1 cited

IVHS via Kuznetsov components and categorical Torelli theorems for weighted hypersurfaces

Xun Lin, Jørgen Vold Rennemo, Shizhuo Zhang

We study the categorical Torelli theorem for smooth (weighted) hypersurfaces in (weighted) projective spaces via the Hochschild--Serre algebra of its Kuznetsov component. In the fi…

math.AG2024

Three approaches to a categorical Torelli theorem for cubic threefolds of non-Eckardt type via the equivariant Kuznetsov components

Sebastian Casalaina-Martin, Xianyu Hu, Xun Lin +2

Let $Y$ be a cubic threefold with a non-Eckardt type involution $τ$ . Our first main result is that the $τ$ -equivariant category of the Kuznetsov component $\mathcal{K}u_{\mathbb{Z}…

math.AG2024

Lagrangian families of Bridgeland moduli spaces from Gushel-Mukai fourfolds

Soheyla Feyzbakhsh, Hanfei Guo, Zhiyu Liu +1

Let $X$ be a very general Gushel-Mukai (GM) variety of dimension $n \geq 4$ , and let $Y$ be a smooth hyperplane section. There are natural pull-back and push-forward functors betwee…

math.AG2024

Linear subspaces of the intersection of two quadrics via Kuznetsov component

Yanjie Li, Shizhuo Zhang

Let $Q_{i} (i = 1, 2)$ be $2 g$ dimensional quadrics in $P^{2 g + 1}$ and let $Y$ be the smooth intersection $Q_{1} \cap Q_{2}$ . We associate the linear subspace in $Y$ with vector bundl…

math.AG2023

Kuznetsov's Fano threefold conjecture via Hochschild-Serre algebra

Xun Lin, Shizhuo Zhang

Let $Y$ be a smooth quartic double solid regarded as a degree 4 hypersurface of the weighted projective space $P (1, 1, 1, 1, 2)$ . We study the multiplication of Hochschild-Ser…

math.AG2023

Serre algebra, matrix factorization and categorical Torelli theorem for hypersurfaces

Xun Lin, Shizhuo Zhang

Let $X$ be a smooth Fano variety. We attach a bi-graded associative algebra $\mathrm{HS}(\mathcal{K}u(X))=\bigoplus_{i,j\in \mathbb{Z}} \mathrm{Hom}(\mathrm{Id},S_{\mathcal{K}u(X)}…

math.AG2023

New perspectives on categorical Torelli theorems for del Pezzo threefolds

Soheyla Feyzbakhsh, Zhiyu Liu, Shizhuo Zhang

Let $Y_{d}$ be a del Pezzo threefold of Picard rank one and degree $d \geq 2$ . In this paper, we apply two different viewpoints to study $Y_{d}$ via a particular admissible subcategory…

math.AG2022★ 2 cited

Brill-Noether reconstruction of index one prime Fano threefolds

Augustinas Jacovskis, Zhiyu Liu, Shizhuo Zhang

We show by a uniform argument that every index one prime Fano threefold $X$ of genus $g \geq 6$ can be reconstructed as a Brill-Noether locus inside a Bridgeland moduli space of sta…

math.AG2022

A moduli theoretic approach to Lagrangian subvarieties of hyperkähler varieties: Examples

Hanfei Guo, Zhiyu Liu, Shizhuo Zhang

We propose two conjectures on a moduli theoretic approach to constructing Lagrangian subvarieties of hyperkähler varieties arising from the Kuznetsov components of cubic fourfolds…

math.AG2022

Infinitesimal categorical Torelli theorems for Fano threefolds

Augustinas Jacovskis, Xun Lin, Zhiyu Liu +1

Let $X$ be a smooth Fano variety and $K u (X)$ the Kuznetsov component. Torelli theorems for $K u (X)$ says that it is uniquely determined by a polarized abelian va…

math.AG2022★ 2 cited

Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli spaces

Hanfei Guo, Zhiyu Liu, Shizhuo Zhang

We identify the double dual EPW sextic $Y_{A^{⊥}}$ and the double EPW sextic $Y_{A}$ , associated with a very general Gushel-Mukai fourfold $X$ , with the B…

math.AG2021★ 10 cited

Categorical Torelli theorems for Gushel-Mukai threefolds

Augustinas Jacovskis, Xun Lin, Zhiyu Liu +1

We show that a general ordinary Gushel-Mukai(GM) threefold $X$ is reconstructed from the Kuznetsov component $K u (X)$ together with an extra data coming from tautological…

math.AG2021★ 2 cited

A note on Bridgeland moduli spaces and moduli spaces of sheaves on $X_{14}$ and $Y_{3}$

Zhiyu Liu, Shizhuo Zhang

We study Bridgeland moduli spaces of semistable objects of $(- 1)$ -classes and $(- 4)$ -classes in the Kuznetsov components on index one prime Fano threefold $X_{4 d + 2}$ of degree $4d+…

math.AG2020★ 4 cited

Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture

Shizhuo Zhang

We study the Hilbert scheme $H$ of twisted cubics on a special smooth Gushel-Mukai threefolds $X_{10}$ . We show that it is a smooth irreducible projective threefold if $X…

math.AG2020★ 2 cited

On cyclic strong exceptional collections of line bundles on surfaces

Alexey Elagin, Junyan Xu, Shizhuo Zhang

We study exceptional collections of line bundles on surfaces. We prove that any full cyclic strong exceptional collection of line bundles on a rational surface is an augmentation i…

A refinement of the strange duality conjecture on K3 surfaces

Orlov's rationality conjecture for surfaces

Categorical Torelli theorem for (weighted) hypersurfaces via singularity category

Categorical reconstruction of del Pezzo surfaces: Hochschild--Serre algebras and spinor modifications

A note on the noncommutative Hodge conjecture for graded matrix factorizations

Categorical resolutions and birational geometry of nodal Gushel-Mukai varieties

EPW varieties as moduli spaces on ordinary GM surfaces and special GM threefolds

Infinitesimal Torelli problems for special Gushel-Mukai and related Fano threefolds: Hodge theoretical and categorical perspectives

Double EPW cubes from twisted cubics on Gushel-Mukai fourfolds

IVHS via Kuznetsov components and categorical Torelli theorems for weighted hypersurfaces

Three approaches to a categorical Torelli theorem for cubic threefolds of non-Eckardt type via the equivariant Kuznetsov components

Lagrangian families of Bridgeland moduli spaces from Gushel-Mukai fourfolds

Linear subspaces of the intersection of two quadrics via Kuznetsov component

Kuznetsov's Fano threefold conjecture via Hochschild-Serre algebra

Serre algebra, matrix factorization and categorical Torelli theorem for hypersurfaces

New perspectives on categorical Torelli theorems for del Pezzo threefolds

Brill-Noether reconstruction of index one prime Fano threefolds

A moduli theoretic approach to Lagrangian subvarieties of hyperkähler varieties: Examples

Infinitesimal categorical Torelli theorems for Fano threefolds

Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli spaces

Categorical Torelli theorems for Gushel-Mukai threefolds

A note on Bridgeland moduli spaces and moduli spaces of sheaves on X14​ and Y3​

Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture

On cyclic strong exceptional collections of line bundles on surfaces

A note on Bridgeland moduli spaces and moduli spaces of sheaves on $X_{14}$ and $Y_{3}$