Gorenstein modifications and \mathds{𝑄}-Gorenstein rings

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2016-11-13 DOI:10.1090/JAG/760

Hailong Dao, O. Iyama, Ryo Takahashi, M. Wemyss

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引用次数: 5

Abstract

Let R R be a Cohen–Macaulay normal domain with a canonical module ω R \omega _R . It is proved that if R R admits a noncommutative crepant resolution (NCCR), then necessarily it is Q \mathds {Q} -Gorenstein. Writing S S for a Zariski local canonical cover of R R , a tight relationship between the existence of noncommutative (crepant) resolutions on R R and S 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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Gorenstein修正和\数学{𝑄}-Gorenstein环

设R R是一个柯恩-麦考利正规定义域，其正则模为R。证明了如果R R允许非交换蠕变分解(NCCR)，则它必然是Q \mathds {Q} -Gorenstein。对R R的Zariski局部正则盖写S S，给出了R R上非交换(渐变)分辨的存在性与S S之间的紧密关系。提出了一个较弱的Gorenstein修正概念，并给出了一个类似的紧密关系。有三种应用:连通约化群的非gorenstein商奇点不允许存在NCCR，任何NCCR的中心都是log-terminal，二维cm有限代数的Auslander-Esnault分类可以由Buchweitz-Greuel-Schreyer导出。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.