Derived equivalences of generalized Kummer varieties

2022/08/23 by Pablo Magni, Magni, Pablo · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2208.11183

openalex publication_date 2022/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study derived (auto)equivalences of generalized Kummer varieties Kumⁿ(A). We provide an answer to a question raised by Namikawa by showing that the generalized Kummer varieties Kumⁿ(A) and Kumⁿ(A^\vee) are derived equivalent as long as n is even and the abelian surface A admits a polarization whose exponent is coprime to n+1. Furthermore we obtain exact sequences involving groups of autoequivalences in the style of Orlov's short exact sequence for autoequivalences of abelian varieties. Finally, we exhibit generalized Kummer fourfolds which are not birationally equivalent but still derived equivalent.

Cited by

• The Lefschetz standard conjectures for 4d-dimensional Kummer-type hyper-Kaehler varieties
• Derived categories of generalized Kummer varieties: extended Mukai vector
• Lifting derived equivalences of abelian surfaces to generalized Kummer varieties

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