Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Orbifold Semiorthogonal Decompositions for Abelian Varieties

Bronson Lim, Franco Rota

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 $G = T\rtimes H$ with $T$ a subgroup of translations and $H$ is a subgroup of group automorphisms.

Orbifold Semiorthogonal Decompositions for Abelian Varieties

Abstract

Suppose is a finite group acting on an Abelian variety such that the coarse moduli space is smooth. Using the recent classification result due to Auffarth, Lucchini Arteche, and Quezada, we construct an orbifold semiorthogonal decomposition for provided with a subgroup of translations and is a subgroup of group automorphisms.

Paper Structure

This paper contains 26 sections, 28 theorems, 122 equations.

Table of Contents

  1. Introduction
  2. Orbifold semiorthogonal decompositions
  3. Main result
  4. Outline of Proof
  5. Outline of Paper
  6. Conventions and notation
  7. Acknowledgements
  8. Preliminaries
  9. Equivariant derived categories
  10. Orbifold semiorthogonal decompositions
  11. Smooth quotients of Abelian varieties
  12. orbifold semiorthogonal decomposition for A2/G(4,4,2)
  13. Representation Theory of G(4,2,2)
  14. Fourier-Mukai kernels
  15. Assembling the Orbifold Semiorthogonal Decomposition
  16. ...and 11 more sections

Key Result

Theorem 1.2

Let $A$ be an Abelian variety and $G=T\rtimes H$ a finite group of automorphisms of $A$ such that the quotient $A/G$ is smooth. Then there exists an orbifold semiorthogonal decomposition for $\mathcal{D}[A/G]$.

Theorems & Definitions (58)

  • Conjecture 1.1: Orbifold Semiorthogonal Decomposition pvdb-equivariant
  • Theorem 1.2: = Theorem \ref{['thm:msod-abelian-vars-full']}
  • Remark 1.3
  • Corollary 1.4
  • Definition 2.1
  • Definition 2.2
  • Remark 2.3
  • Remark 2.4
  • Example 2.5
  • Theorem 2.6: ga-smooth1
  • ...and 48 more