On exceptional quotient singularities

TL;DR

This paper investigates exceptional quotient singularities, establishing a criterion based on Tian's alpha-invariant, and classifies such singularities in four and five dimensions.

Contribution

It introduces an exceptionality criterion using the alpha-invariant and applies it to classify higher-dimensional exceptional quotient singularities.

Findings

Established a criterion for exceptionality via the alpha-invariant.

Classified four-dimensional and five-dimensional exceptional quotient singularities.

Abstract

We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the $\alpha$-invariant of Tian, and utilize it to classify four-dimensional and five-dimensional exceptional quotient singularities.