Non-commutative crepant resolutions for some toric singularities II

2017/07/25 by Špela Špenko, Michel Van den Bergh, Špenko, Špela +1 · 3 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AG #math.RA

paper · pdf · doi:10.48550/arxiv.1707.08245

Fix an undefined notation

arxiv created 2018/07/23 · arxiv updated 2018/07/24

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.

Cited by

• Non-commutative crepant resolutions of toric singularities with divisor class group of rank one
• Weak del Pezzo surfaces yield 2-hereditary algebras and 3-Calabi-Yau algebras
• 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