Rank One Bridgeland Stable Moduli Spaces on A Principally Polarized Abelian Surface

TL;DR

This paper computes and describes the geometry of Bridgeland stable moduli spaces on a principally polarized abelian surface, using Fourier-Mukai techniques to analyze wall-crossings as Mukai flops and establishing projectivity.

Contribution

It extends the understanding of Bridgeland stability conditions on abelian surfaces by explicitly computing moduli spaces and describing wall-crossings as Mukai flops.

Findings

Moduli spaces are projective.

Wall-crossings correspond to Mukai flops.

Explicit description of moduli spaces for twisted ideal sheaves.

Abstract

We compute moduli spaces of Bridgeland stable objects on an irreducible principally polarized complex abelian surface corresponding to twisted ideal sheaves. We use Fourier-Mukai techniques to extend the ideas of Arcara and Bertram to express wall-crossings as Mukai flops and show that the moduli spaces are projective.