Three-dimensional isolated quotient singularities in odd characteristic

2012/10/30 by Stepanov, D. A.
#13A50 #14B05 #14L30 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1210.8006

Abstract

Let a finite group G act linearly on a finite dimensional vector space V over an algebraically closed field k of characteristic p>2. Assume that the quotient V/G is an isolated singularity. In the case when p does not divide the order of G, isolated singularities V/G are completely classified and their classification reduces to Zassenhaus-Vincent-Wolf classification of isolated quotient singularities over the field of complex numbers. In the present paper we show that if dimension of V is 3, then also in the modular case (p divides the order of G) classification of isolated quotient singularities reduces to Zassenhaus-Vincent-Wolf classification. Some remarks on modular quotient singularities in other dimensions and in even characteristic are also given.

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