Author

Shi-Zhuo Zhang

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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

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