Lifting derived equivalences of abelian surfaces to generalized Kummer varieties
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914368892960768 |
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| author | Yang, Yuxuan |
| author_facet | Yang, Yuxuan |
| contents | In this article, we study the $G$-autoequivalences of the derived category $\mathbf{D}^b_G(A)$ of $G$-equivariant objects for an abelian variety $A$ with $G$ being a finite subgroup of $\mathrm{Pic}^0(A)$. We provide a result analogue to Orlov's short exact sequence for derived equivalences of abelian varieties. It can be generalized to the derived equivalences of abelian varieties for a same $G$ in general. Furthermore, we find derived equivalences of generalized Kummer varieties by lifting derived equivalences of abelian surfaces using the $G$-equivariant version of Orlov's short exact sequence and some ``splitting" propositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11358 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lifting derived equivalences of abelian surfaces to generalized Kummer varieties Yang, Yuxuan Algebraic Geometry 14J42(Primary), 18A05 (Secondary) In this article, we study the $G$-autoequivalences of the derived category $\mathbf{D}^b_G(A)$ of $G$-equivariant objects for an abelian variety $A$ with $G$ being a finite subgroup of $\mathrm{Pic}^0(A)$. We provide a result analogue to Orlov's short exact sequence for derived equivalences of abelian varieties. It can be generalized to the derived equivalences of abelian varieties for a same $G$ in general. Furthermore, we find derived equivalences of generalized Kummer varieties by lifting derived equivalences of abelian surfaces using the $G$-equivariant version of Orlov's short exact sequence and some ``splitting" propositions. |
| title | Lifting derived equivalences of abelian surfaces to generalized Kummer varieties |
| topic | Algebraic Geometry 14J42(Primary), 18A05 (Secondary) |
| url | https://arxiv.org/abs/2507.11358 |