ON SMOOTHNESS OF MINIMAL MODELS OF QUOTIENT SINGULARITIES BY FINITE SUBGROUPS OF SL n(?)
ON SMOOTHNESS OF MINIMAL MODELS OF QUOTIENT SINGULARITIES BY FINITE SUBGROUPS OF SL n(?)
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论SL n(?)有限子群的商奇异性极小模型的光滑性
DOI：
10.1017/s0017089517000325
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发表时间：
2018
影响因子：
0.5
通讯作者：
YAMAGISHI RYO
中科院分区：
文献类型：
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作者：
Takayuki Ohara;Akiko Satake;YAMAGISHI RYO
证明了有限子群G的商奇性ℂn/G仅当G由次元生成时，⊂sLn(ℂ)才有初等解.这是Verbitsky(Asian J.Math.4(3)(2000)，553-563)的结果的推广。我们还给出了由G的信息显式计算给定ℂn/G的极小模型的COX环的方法。作为应用，我们研究了一些商奇性的极小模型的光滑性。与Bellamy和Schedler的工作一起，完成了允许射影辛解的辛非本原商奇点的分类。
We prove that a quotient singularity ℂn/G by a finite subgroup G ⊂ SLn(ℂ) has a crepant resolution only if G is generated by junior elements. This is a generalization of the result of Verbitsky (Asian J. Math.4(3) (2000), 553–563). We also give a procedure to compute the Cox ring of a minimal model of a given ℂn/G explicitly from information of G. As an application, we investigate the smoothness of minimal models of some quotient singularities. Together with work of Bellamy and Schedler, this completes the classification of symplectically imprimitive quotient singularities that admit projective symplectic resolutions.