Crepant resolutions and brane tilings I: Toric realization

Details Crepant resolutions and brane tilings I: Toric realization Crepant resolutions and brane tilings I: Toric realization

2009-08-24

arxiv.org/abs/0908.3475v2

Mathematics

Algebraic Geometry

22 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. In this paper we study its commutative
and non-commutative crepant resolutions. We give an explicit toric description
of all its commutative crepant resolutions. We also explain how the McKay
correspondence in dimension 3 can be interpreted using brane tilings.

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