On smoothness of minimal models of quotient singularities by finite subgroups of SL_n(ℂ)

2016/02/04 by Ryo Yamagishi, Yamagishi, Ryo · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1602.01572

openalex publication_date 2016/02/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that a quotient singularity ℂⁿ/G by a finite subgroup G⊂ SL_n(ℂ) has a crepant resolution only if G is generated by junior elements. This is a generalization of the result of Verbitsky [V]. 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 which admit projective symplectic resolutions.

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• Systems of imprimitivity for rank two quaternionic reflection groups

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