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

Zheng Hua

Vol. 277 (2015), No. 1, 119–147

DOI: 10.2140/pjm.2015.277.119

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.

Keywords

algebraic geometry, derived category, Donaldson–Thomas theory

Mathematical Subject Classification 2010

Primary: 14F05, 14N35

Milestones

Received: 23 May 2014

Revised: 27 January 2015

Accepted: 2 February 2015

Published: 6 August 2015