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arXiv · 2301.05052

Matrix factorization for quasi-homogeneous singularities

Ananyo Dan·Agustín Romano-Velázquez
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Abstract

Given an isolated, quasi-homogeneous singularity $X$ we prove that there is a group isomorphism between the group of rank one reflexive sheaves on $X$ and the free abelian group generated by $\mathbb{C}^*$-divisors, modulo linear equivalence. When $\dim(X)=2$ we reduce the problem of finding matrix factorizations of arbitrary reflexive $\mathcal{O}_X$-modules to the same question on rank one reflexive sheaves. We then enumerate the matrix factorizations of all rank one reflexive sheaves. As a consequence, we prove a conjecture of Etingof and Ginzburg on point modules.

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Ananyo Dan, Agustín Romano-Velázquez. 2023-01-12. Matrix factorization for quasi-homogeneous singularities. https://arxiv.org/abs/2301.05052

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