Gorenstein modifications and Q-Gorenstein rings
Journal of Algebraic Geometry, ISSN: 1534-7486, Vol: 29, Issue: 4, Page: 729-751
2020
- 6Citations
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Metrics Details
- Citations6
- Citation Indexes6
- CrossRef1
Article Description
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.
Bibliographic Details
American Mathematical Society (AMS)
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