Donaldson-Thomas invariants vs. intersection cohomology for categories of homological dimension one (1512.03343v1)

Abstract: The present paper is an extension of a previous paper written in collaboration with Markus Reineke dealing with quiver representations. The aim of the paper is to generalize the theory and to provide a comprehensive theory of Donaldson-Thomas invariants for abelian categories of homological dimension one (without potential) satisfying some technical conditions. The theory will apply for instance to representations of quivers, coherent sheaves on smooth projective curves, and some coherent sheaves on smooth projective surfaces. We show that the (motivic) Donaldson-Thomas invariants satisfy the Integrality conjecture and identify the Hodge theoretic version with the (compactly supported) intersection cohomology of the corresponding moduli spaces of objects. In fact, we deal with a refined version of Donaldson-Thomas invariants which can be interpreted as classes in the Grothendieck group of some "sheaf" on the moduli space. In particular, we reproduce the intersection complex of moduli spaces using Donaldson-Thomas theory.