Donaldson-Thomas invariants via microlocal geometry

TL;DR

This paper establishes that Donaldson-Thomas invariants are equivalent to weighted Euler characteristics of moduli spaces, highlighting their dependence solely on scheme structure, and introduces generalized invariants for open moduli spaces.

Contribution

It proves the equivalence of Donaldson-Thomas invariants and weighted Euler characteristics, and introduces new invariants for moduli problems with open spaces.

Findings

Donaldson-Thomas invariants equal weighted Euler characteristics

Invariants depend only on scheme structure, not obstruction theory

New invariants for stratified moduli spaces

Abstract

We prove that Donaldson-Thomas type invariants are equal to weighted Euler characteristics of their moduli spaces. In particular, such invariants depend only on the scheme structure of the moduli space, not the symmetric obstruction theory used to define them. We also introduce new invariants generalizing Donaldson-Thomas type invariants to moduli problems with open moduli space. These are useful for computing Donaldson-Thomas type invariants over stratifications.