Singularity categories and singular loci of certain quotient singularities

Xiaojun Chen; Jieheng Zeng

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arXiv · 2411.15389

Singularity categories and singular loci of certain quotient singularities

Xiaojun Chen·Jieheng Zeng

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Abstract

Let $V$ be a finite dimensional $k$-vector space, where $k$ is an algebraic closed field of characteristic zero. Let $G \subseteq \mathrm{SL}(V)$ be a finite abelian group, and denote by $S$ the $G$-invariant subring of the polynomial ring $k[V]$. It is shown that the singularity category $D_{sg}(S)$ recovers the reduced singular locus of $\mathrm{Spec}(S)$.

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Xiaojun Chen, Jieheng Zeng. 2024-11-23. Singularity categories and singular loci of certain quotient singularities. https://arxiv.org/abs/2411.15389

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