Gorenstein modifications and Q-Gorenstein rings

Dao, H., Iyama, O., Takahashi, R. and Wemyss, M. (2020) Gorenstein modifications and Q-Gorenstein rings. Journal of Algebraic Geometry, (doi: 10.1090/jag/760) (Early Online Publication)

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Abstract

Let R be a Cohen–Macaulay normal domain with a canonical module ωR. It is proved that if R admits a noncommutative crepant resolution (NCCR), then necessarily it is Q-Gorenstein. Writing S for a Zariski local canonical cover of R, a tight relationship between the existence of noncommutative (crepant) resolutions on R and S is given. A weaker notion of Gorenstein modification is developed, and a similar tight relationship is given. There are three applications: non-Gorenstein quotient singularities by connected reductive groups cannot admit an NCCR, the centre of any NCCR is log-terminal, and the Auslander–Esnault classification of two-dimensional CM-finite algebras can be deduced from Buchweitz–Greuel–Schreyer.

Item Type:Articles
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Wemyss, Professor Michael
Authors: Dao, H., Iyama, O., Takahashi, R., and Wemyss, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Algebraic Geometry
Publisher:American Mathematical Society
ISSN:1056-3911
ISSN (Online):1534-7486
Published Online:31 March 2020
Copyright Holders:Copyright © 2020 University Press, Inc.
First Published:First published in Journal of Algebraic Geometry 2020
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
173986The Homological Minimal Model ProgramMichael WemyssEngineering and Physical Sciences Research Council (EPSRC)EP/K021400/2M&S - Mathematics