Chern-Simons functions on toric Calabi-Yau threefolds and Donaldson-Thomas theory

Abstract

We use the notion of strong exceptional collections to give a construction of the global Chern–Simons functions for toric Calabi–Yau stacks of dimension three. Moduli spaces of sheaves on such stacks can be identified with critical loci of these functions. We give two applications of these functions. First, we prove Joyce’s integrality conjecture of generalized DT invariants on local surfaces. Second, we prove a dimension reduction formula for virtual motives, which leads to a recursion formula for motivic Donaldson–Thomas invariants.