Singularity categories and singular loci of certain quotient singularities
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914096965746688 |
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| author | Chen, Xiaojun Zeng, Jieheng |
| author_facet | Chen, Xiaojun Zeng, Jieheng |
| contents | 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 $\mathrm{Spec}(S)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singularity categories and singular loci of certain quotient singularities Chen, Xiaojun Zeng, Jieheng Algebraic Geometry Rings and Algebras Representation Theory 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 $\mathrm{Spec}(S)$. |
| title | Singularity categories and singular loci of certain quotient singularities |
| topic | Algebraic Geometry Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2411.15389 |