Normal surface singularities admitting contracting automorphisms

TL;DR

This paper proves that complex normal surface singularities with contracting automorphisms are quasihomogeneous and explores the geometry of the resulting orbit space on compact complex surfaces.

Contribution

It establishes the quasihomogeneity of singularities with contracting automorphisms and characterizes the geometry of their orbit spaces.

Findings

Singularities with contracting automorphisms are quasihomogeneous.

The geometry of the orbit space of such automorphisms is described.

Provides a classification framework for these singularities.

Abstract

We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting automorphism.