Quotient singularities by permutation actions are canonical

TL;DR

This paper proves that quotient varieties from permutation representations of finite groups have only canonical singularities in any characteristic, with specific conditions on Kawamata log terminal and log canonical singularities.

Contribution

It establishes the nature of singularities for quotient varieties from permutation group actions across all characteristics, extending previous understanding.

Findings

Quotient varieties have only canonical singularities in arbitrary characteristic.

The associated log pair is Kawamata log terminal except in characteristic two.

The log pair is log canonical in arbitrary characteristic.

Abstract

The quotient variety associated to a permutation representation of a finite group has only canonical singularities in arbitrary characteristic. Moreover, the log pair associated to such a representation is Kawamata log terminal except in characteristic two, and log canonical in arbitrary characteristic.