Pathological quotient singularities in characteristic three which are not log canonical

2018/11/14 by Takahiro Yamamoto, Yamamoto, Takahiro
Mathematics · #14B05 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14B05

paper · pdf · doi:10.48550/arxiv.1811.05620

v2: revision according to comments of a referee, changed the title

arxiv created 2019/10/04 · arxiv updated 2019/10/07

Abstract

In characteristic zero, quotient singularities are log terminal. Moreover, we can check whether a quotient variety is canonical or not by using only the age of each element of the relevant finite group if the group does not have pseudo-reflections. In positive characteristic, a quotient variety is not log terminal, in general. In this paper, we give an example of the quotient variety which is not log terminal such that the quotient varieties associated to any proper subgroups are canonical. In particular, we cannot determine whether a given quotient singularity is canonical by looking at proper subgroups.

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