Xun Lin

activity

20222026

most citedIVHS via Kuznetsov components and categorical Torelli theorems for weighted hypersurfaces

1 citations · 1 across the 9 of their papers we have counts for

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11 papers · 1 filter

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

Group action of Hochschild-Serre algebra and categorical reconstruction

Xun Lin

We study the action of the Serre functor of smooth proper dg categories at their Hochschild-Serre algebra, and the invariant sub-aglebra of the Serre functor. As applications, we p…

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.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.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.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.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…