Singularities Admitting Contracting Automorphisms

TL;DR

This paper proves that complex analytic singularities with a contracting automorphism are necessarily quasi-homogeneous, revealing a deep connection between symmetry and singularity structure.

Contribution

It establishes that the existence of a contracting automorphism implies the singularity is quasi-homogeneous, a new characterization linking automorphisms to singularity types.

Findings

Contracting automorphisms imply quasi-homogeneity of singularities

Quasi-homogeneity characterized by automorphism properties

Automorphisms influence the geometric structure of singularities

Abstract

Given a complex analytic singularity $(X, 0)$, we show that if there exists an automorphism $F: (X, 0) \to (X, 0)$ that is contracting, then $(X, 0)$ is quasi-homogeneous.