Weakly-exceptional quotient singularities in prime dimension

TL;DR

This paper investigates weakly-exceptional quotient singularities in prime dimensions, extending classification results beyond the previously studied dimensions up to five, to arbitrary prime dimensions.

Contribution

It generalizes the classification of weakly-exceptional quotient singularities to all prime dimensions, expanding understanding of their structure in higher dimensions.

Findings

Classification extended to arbitrary prime dimensions

Identified unique properties of singularities in prime dimensions

Provided new insights into the structure of quotient singularities

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 $5$. This paper looks at such singularities in dimension $p$, where $p$ is an arbitrary prime number.