Journal of Noncommutative Geometry
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Published online: 2020-05-18
Non-commutative crepant resolutions for some toric singularities. IIŠpela Špenko and Michel Van den Bergh (1) Université libre de Bruxelles, Belgium
(2) Hasselt University, Diepenbeek, Belgium
Using the theory of dimer models Broomhead proved that every 3-dimensional Gorenstein affine toric variety Spec $R$ admits a toric non-commutative crepant resolution (NCCR). We give an alternative proof of this result by constructing a tilting bundle on a (stacky) crepant resolution of Spec $R$ using standard toric methods. Our proof does not use dimer models.
Keywords: Toric varieties, tilting bundle, noncommutative resolution
Špenko Špela, Van den Bergh Michel: Non-commutative crepant resolutions for some toric singularities. II. J. Noncommut. Geom. 14 (2020), 73-103. doi: 10.4171/JNCG/359