Five-Dimensional Weakly Exceptional 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 most $4$. This note extends that classification to dimension $5$.

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