Five-Dimensional Weakly Exceptional Quotient Singularities

TL;DR

This paper extends the classification of five-dimensional weakly-exceptional quotient singularities, a class of singularities with unique log terminal blow-ups, from lower dimensions to dimension five.

Contribution

It provides the first classification of five-dimensional weakly-exceptional quotient singularities, expanding the understanding of these singularities beyond dimension four.

Findings

Classification of 5D weakly-exceptional quotient singularities completed

Extension of previous 4D classifications to 5D

New insights into higher-dimensional singularity structures

Abstract

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow up. This is a natural generalization of the surface singularities of types $D_{n}$, $E_{6}$, $E_{7}$ and $E_{8}$. Since this idea was introduced, quotient singularities of this type have been classified in dimensions up to most $4$. This note extends that classification to dimension $5$.