Lifting derived equivalences of abelian surfaces to generalized Kummer varieties

2025/07/15 by Yang, Yuxuan · 2 citations
#14J42(Primary) #18A05 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.11358

Abstract

In this article, we study the G-autoequivalences of the derived category D^b_G(A) of G-equivariant objects for an abelian variety A with G being a finite subgroup of Pic⁰(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.

Citations

• Derived equivalences of generalized Kummer varieties
• Kuznetsov's Fano threefold conjecture via K3 categories and enhanced group actions
• Abelianisation of orthogonal groups and the fundamental group of modular varieties
• Mukai implies McKay: the McKay correspondence as an equivalence of derived categories

Cited by

• The Lefschetz standard conjectures for 4d-dimensional Kummer-type hyper-Kaehler varieties
• Derived categories of generalized Kummer varieties: extended Mukai vector

Related

• Derived equivalences of generalized Kummer varieties
• Derived categories and Kummer varieties
• A note on Fourier-Mukai partners of abelian varieties over positive characteristic fields
• New derived autoequivalences of Hilbert schemes and generalised Kummer varieties
• Derived categories of sheaves: a skimming