A short proof that equisingular plane curve singularities are topologically equivalent

TL;DR

This paper proves that equisingular plane curve singularities are topologically equivalent, extending previous results to a broader class of singularities using a method originally applied to irreducible cases.

Contribution

It generalizes the topological equivalence of equisingular plane curve singularities beyond irreducible cases, employing a method by P. Fortuny Ayuso.

Findings

Equisingular plane curve singularities are topologically equivalent.

The proof extends previous irreducible cases to general cases.

The method used is based on P. Fortuny Ayuso's approach.

Abstract

We prove that if two plane curve singularities are equisingular, then they are topologically equivalent. The method we will use is P.~Fortuny~Ayuso's who proved this result for irreducible plane curve singularities.