Non reduced plane curve singularities with $b_1(F)=0$ and Bobadilla's question

TL;DR

This paper investigates plane curve singularities with Milnor fibers having zero first Betti number, showing that such singularities are equivalent to simple monomials like x^r, addressing a specific question in the field.

Contribution

It characterizes plane curve singularities with trivial Milnor fiber first Betti number, providing a classification that confirms a particular case of Bobadilla's question.

Findings

Milnor fiber's first Betti number zero implies the singularity is equivalent to x^r.

Provides a classification of such singularities.

Addresses Bobadilla's question in this specific context.

Abstract

If the first Betti number of the Milnor fibre of a plane curve singularity is zero, then the defining function is equivalent to $x^r$.