Dao, H., Iyama, O., Takahashi, R. and Wemyss, M. (2020) Gorenstein modifications and Q-Gorenstein rings. Journal of Algebraic Geometry, 29(4), pp. 729-751. (doi: 10.1090/jag/760)
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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: | Published |
| 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 29(4): 729-751 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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