Orbifold Semiorthogonal Decompositions for Abelian Varieties

Abstract

Suppose $G$ is a finite group acting on an Abelian variety $A$ such that the coarse moduli space $A/G$ is smooth. Using the recent classification result due to Auffarth, Lucchini Arteche, and Quezada, we construct an orbifold semiorthogonal decomposition for $\mathcal{D}[A/G]$ provided $G=T⋊H$ with $T$ a subgroup of translations and $H$ is a subgroup of group automorphisms.

v1: 21 pages, comments welcome! v2: 25 pages. Title changed, details added in Section 4, improved overall exposition and references updated. Accepted manuscript, to appear in J. noncommut. geom