Pathological Quotient Singularities in Characteristic Three Which Are Not Log Canonical

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 pseudoreflections. In positive characteristic, a quotient variety is not log terminal in general. In this paper, we give an example of a quotient variety that is not log terminal such that the quotient varieties associated with any proper subgroups are canonical. In particular, we cannot determine whether a given quotient singularity is canonical by looking at proper subgroups.