Donaldson-Thomas invariants for complexes on abelian threefolds

TL;DR

This paper develops a new approach to defining Donaldson-Thomas invariants for complexes on abelian threefolds, extending existing theories to include fixed determinants and Fourier-Mukai transforms.

Contribution

It introduces a modified perfect symmetric obstruction theory for complexes on abelian threefolds, enabling the definition of nontrivial Donaldson-Thomas invariants in this setting.

Findings

Defined Donaldson-Thomas invariants for complexes on abelian threefolds

Extended the obstruction theory to include fixed determinant and Fourier-Mukai conditions

Established nontrivial invariants for moduli spaces modulo twist and translation

Abstract

We modify the standard perfect symmetric obstruction theory for moduli spaces of simple perfect complexes, to the situation of complexes on abelian threefolds with fixed determinant and Fourier-Mukai determinant. As outcome we attach nontrivial Donaldson-Thomas invariants to moduli spaces for complexes modulo twist and translation.