Crepant resolutions and brane tilings II: Tilting bundles

Abstract

Given a brane tiling, that is, a bipartite graph on a torus, we can associate with it a singular 3-Calabi-Yau variety. Using the brane tiling, we can also construct all crepant resolutions of the above variety. We give an explicit toric description of tilting bundles on these crepant resolutions. This result proves the conjecture of Hanany, Herzog and Vegh and a version of the conjecture of Aspinwall.

15 pages

References in corpus (4)

• On moduli spaces of quiver representations associated with dimer models
• On the noncommutative Donaldson-Thomas invariants arising from brane tilings
• Crepant resolutions and brane tilings I: Toric realization
• D-Branes on Toric Calabi-Yau Varieties