Counting sheaves on Calabi-Yau and abelian threefolds

TL;DR

This paper surveys the foundational aspects of Donaldson-Thomas invariants for stable sheaves on algebraic threefolds, focusing on Calabi-Yau and abelian threefolds, highlighting their mathematical significance.

Contribution

It provides a comprehensive overview of the foundational theory of Donaldson-Thomas invariants specifically for abelian threefolds and Calabi-Yau threefolds, emphasizing the case of trivial canonical bundle.

Findings

Clarifies the mathematical framework for Donaldson-Thomas invariants on these threefolds.

Highlights the importance of stability conditions in defining invariants.

Provides insights into the geometric and algebraic structures involved.

Abstract

We survey the foundations for Donaldson-Thomas invariants for stable sheaves on algebraic threefolds with trivial canonical bundle, with emphasis on the case of abelian threefolds.