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Gorenstein modifications and Q-Gorenstein rings

Journal of Algebraic Geometry, ISSN: 1534-7486, Vol: 29, Issue: 4, Page: 729-751
2020
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  • Citations
    6
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      6

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.

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