Refined open noncommutative Donaldson–Thomas invariants for small crepant resolutions

Kentaro Nagao

Vol. 254 (2011), No. 1, 173–209

DOI: 10.2140/pjm.2011.254.173

Abstract

We study analogs of noncommutative Donaldson–Thomas invariants corresponding to the refined topological vertex for small crepant resolutions of toric Calabi–Yau 3-folds. We give three definitions of the invariants which are equivalent to each others and provide “wall-crossing” formulas for the invariants. In particular, we get normalized generating functions which are unchanged under wall-crossing.

Keywords

Donaldson–Thomas theory, dimer model, topological vertex

Mathematical Subject Classification 2000

Primary: 14N10, 14N35

Milestones

Received: 13 November 2009

Revised: 2 February 2010

Accepted: 19 March 2010

Published: 7 February 2012