Author

Xun Lin

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Preprint Sep 2026

Categorical Torelli theorem for (weighted) hypersurfaces via singularity category

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 Kuznetsov component, whereas for hypersurfaces of general type we use the full category of graded matrix factorizations. When the degree is coprime...

Xun Lin, Jie-Heng Zeng, Shi-Zhuo Zhang · 1 citation

Preprint Sep 2026

Group action of Hochschild-Serre algebra and categorical reconstruction

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 prove some theorems of categorical Torelli. Namely, let $\Ku(\X)$ be the Kuznetsov component of degree $d$ smooth hypersurface in weighted pr...

Xun Lin · 1 citation · ⚡1

Preprint Sep 2026

A note on the noncommutative Hodge conjecture for graded matrix factorizations

Let $m\geq 2$ and $d\geq 7$. We consider homogeneous polynomials in $2m+2$ variables of the form $f=F_0(u_0,v_0)+\cdots+F_m(u_m,v_m)$, where the $F_i$ are independently very general squarefree binary forms of degree $d$. We prove the rational noncommutative Hodge conjecture for the dg category $\mathrm{MF}^{\mathrm{gr}...

Xun Lin, Shi-Zhuo Zhang · 0 citations