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ON SMOOTHNESS OF MINIMAL MODELS OF QUOTIENT SINGULARITIES BY FINITE SUBGROUPS OF SLn(ℂ)

Published online by Cambridge University Press:  28 January 2018

RYO YAMAGISHI
RYO YAMAGISHI*
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwakecho, Kyoto, 606-8502, Japan e-mail: ryo-yama@math.kyoto-u.ac.jp
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Abstract

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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 3 , September 2018 , pp. 603 - 634
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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