2009/08/24 by Sergey Mozgovoy, Mozgovoy, Sergey
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.0908.3475
22 pages
arxiv created 2009/08/26 · arxiv updated 2009/12/01
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.