Toric NCCRs for Gorenstein toric singularities with rank-one divisor class group are classified bijectively by non-trivial upper sets in a quotient of the class group and shown to be connected by Iyama-Wemyss mutations, with the number of summands matching the normalized volume of the associated d+2
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Non-commutative crepant resolutions of toric singularities with divisor class group of rank one
Toric NCCRs for Gorenstein toric singularities with rank-one divisor class group are classified bijectively by non-trivial upper sets in a quotient of the class group and shown to be connected by Iyama-Wemyss mutations, with the number of summands matching the normalized volume of the associated d+2