Non-commutative crepant resolutions for some toric singularities I
\v{S}pela \v{S}penko, Michel Van den Bergh
TL;DR
This paper establishes criteria for the existence of non-commutative crepant resolutions in certain toric singularities, confirming known results in three dimensions and extending to some four-dimensional cases.
Contribution
It provides a new criterion for NCCRs in toric singularities and demonstrates their existence in cases previously not known to admit toric NCCRs.
Findings
Confirmed NCCRs for 3D toric Gorenstein singularities
Established NCCRs for some 4D toric Gorenstein singularities
Extended understanding of NCCRs beyond toric cases
Abstract
We give a criterion for the existence of non-commutative crepant resolutions (NCCR's) for certain toric singularities. In particular we recover Broomhead's result that a 3-dimensional toric Gorenstein singularity has a NCCR. Our result also yields the existence of a NCCR for a 4-dimensional toric Gorenstein singularity which is known to have no toric NCCR.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Neurosurgical Procedures and Complications