Automorphism Groups for Quasi-homogeneous Gorenstein Surface Singularities

Let (X, 0) be a non–log-canonical, quasi-homogeneous surface singularity germ. And letG Aut(X, 0) be the maximal reductive subgroup. In this paper we bound the order ofG/C* by −P • P, a purely topological invariant. Hurwitzʹs theorem comes out as a corollary. We use the standard approach of taking the quotient space of (X, 0) by the action of a finite group of automorphisms acting freely onX − {0}.