Non-commutative crepant resolutions for some toric singularities

Špela Špenko; Michel Van den Bergh

doi:10.1093/imrn/rnaa006

Non-commutative crepant resolutions for some toric singularities

Špela Špenko, Michel Van den Bergh

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	8120-8138
Number of pages	19
Journal	International Mathematics Research Notices
Volume	2020
Issue number	21
DOIs	https://doi.org/10.1093/imrn/rnaa006
Publication status	Published - 1 Nov 2020

Bibliographical note

Funding Information:
This work was supported by EPSRC grant [EP/M008460/1 to S.S.]; M.V.D.B. is a senior researcher at the Research Foundation Flanders (FWO). While working on this project he was supported by the FWO grant G0D8616N: “Hochschild cohomology and deformation theory of triangulated categories.”

Publisher Copyright:
© 2020 The Author(s) 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

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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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N2 - 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.

AB - 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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Non-commutative crepant resolutions for some toric singularities

Abstract

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