Non-commutative crepant resolutions for some toric singularities II

2017/07/25 by Špenko, Špela, Bergh, Michel Van den · 3 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1707.08245

Abstract

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.

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• Non-commutative crepant resolutions of toric singularities with divisor class group of rank one
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• Window categories for a simple 9-fold flop of Grassmannian type

Related

• Non-commutative crepant resolutions for some toric singularities I
• Generating toric noncommutative crepant resolutions
• Towards non-commutative crepant resolutions of affine toric Gorenstein varieties
• Semi-steady non-commutative crepant resolutions via regular dimer models
• Non-commutative crepant resolutions of toric singularities with divisor class group of rank one