Journal of Noncommutative Geometry

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Volume 14, Issue 1, 2020, pp. 73–103
DOI: 10.4171/JNCG/359

Published online: 2020-05-18

Non-commutative crepant resolutions for some toric singularities. II

Špela Špenko[1] and Michel Van den Bergh[2]

(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