Crepant resolutions and brane tilings II: Tilting bundles

Details Crepant resolutions and brane tilings II: Tilting bundles Crepant resolutions and brane tilings II: Tilting bundles

2009-09-10

arxiv.org/abs/0909.2013v1

Mathematics

Algebraic Geometry

15 pages

Scientific paper

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.

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