Gorenstein isolated quotient singularities over \(\mathbb{C}\) (Q2921047)

A review about the classifiction of isolated quotient singularities over \(\mathbb{C}\), i.e. singularities of the form \(\mathbb{C}^N/G\), \(G\subseteq \text{ GL}_N(\mathbb{C})\) a finite subgroup, is given. This is the basis of the description of the Gorenstein isolated quotient singularities. This includes a generalization of the following theorem of Kurano and Nishi: Let \(G\) be a finite subgroup of GL\(_p (\mathbb{C})\), \(p>2\) prime and \(\mathbb{C}^p/G\) an isolated Gorenstein singularity. Then \(\mathbb{V}^p/G\) is a cyclic quotient singularity.