On the classification of rational surface singularities

TL;DR

This paper presents a comprehensive classification method for rational surface singularities, extending previous results to multiplicity 8 and analyzing the complexity of their resolution graphs.

Contribution

It introduces a new classification strategy for rational surface singularities and fully classifies certain graph types, extending the known classification to higher multiplicities.

Findings

Classified certain types of rational surface singularity graphs.

Extended classification of rational singularities to multiplicity 8.

Analyzed the complexity of rational resolution graphs.

Abstract

A general strategy is given for the classification of graphs of rational surface singularities. For each maximal rational double point configuration we investigate the possible multiplicities in the fundamental cycle. We classify completely certain types of graphs. This allows to extend the classification of rational singularities to multiplicity 8. We also discuss the complexity of rational resolution graphs.