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arXiv · 2507.11358

Lifting derived equivalences of abelian surfaces to generalized Kummer varieties

Yuxuan Yang
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Abstract

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.

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Yuxuan Yang. 2025-07-15. Lifting derived equivalences of abelian surfaces to generalized Kummer varieties. https://arxiv.org/abs/2507.11358

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