The multiplicity of abelian covers of splice quotient singularities

TL;DR

This paper introduces a method to compute the multiplicity of abelian coverings of splice quotient surface singularities using their resolution graph and Galois group, expanding understanding of their analytic invariants.

Contribution

It provides a novel computational approach for determining the multiplicity of abelian covers in splice quotient singularities based on resolution graph data.

Findings

Method to compute multiplicity from resolution graph and Galois group

Applicable to a class of surface singularities called splice quotients

Enhances the understanding of analytic invariants in singularity theory

Abstract

From a resolution graph with certain conditions, Neumann and Wahl constructed an equisingular family of surface singularities called splice quotients. For this class some fundamental analytic invariants have been computed from their resolution graph. In this paper we give a method to compute the multiplicity of an abelian covering of a splice quotient from its resolution graph and the Galois group.