Uniformization of Cyclic Quotients of Multiplicative A-singularities

Journal of Mathematical Sciences

Takamura, Shigeru¹  Sasaki, Kenjiro¹ 

关键词: Uniformization of singularity;    Monodromy;    Degeneration of Riemann surfaces;    Fractional Dehn twist;    Small group;    Pseudo-reflection group;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

ThisworkismotivatedbythecanonicalmodelofdegenerationsofRiemannsurfaces.Foraquotientspace$A_{d-1}/Gm$ofa`multiplicative'$A$-singularity$A_{d-1}$in$C^{n+1}$underacertaincyclicgroupaction$Gm$on$A_{d-1}$,we{itexplicitly}constructasmallfiniteabeliansubgroup$G$of$GL(n,,C)$suchthat$A_{d-1}/GmcongC^n/G$.Aresolutionof$C^n/G$givesadecompositionofthemonodromy(a{ithigher-dimensionalfractionalDehntwist})ofadegeneration$A_{d-1}/GmoC$intosubtwistsalongtheexceptionalset(itseemsthatT.Ashikaga'sworkonresolutionsisrelatedtothis).Moreover:(1)Wegiveanumericalcriterionforacertainsubgroupof$GL(n,C)$tobesmall.(2)Foracertainfamilyofsubgroupsof$GL(n,,C)$,weshowthatifonesubgroupofthisfamilyissmall,thenallsubgroupsofthisfamilyaresmall{it$($equi-smallnesstheorem$)$}.

【 授权许可】

Unknown