Toric NCCRs of rank-one class-group Gorenstein toric singularities are classified by non-trivial upper sets in a quotient of the class group with a natural partial order.
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Non-commutative crepant resolutions of toric singularities with divisor class group of rank one
Toric NCCRs of rank-one class-group Gorenstein toric singularities are classified by non-trivial upper sets in a quotient of the class group with a natural partial order.