Newton weighted-L\^e-Yomdin polynomials and $\mu$-Zariski pairs of surface singularities

TL;DR

This paper studies a special class of surface singularities defined by weighted-L extsuperscript{e}-Yomdin polynomials and introduces a method to construct new $ppa$-Zariski pairs, advancing understanding of their classification.

Contribution

It develops a novel approach to construct $ppa$-Zariski pairs of surface singularities using Newton weighted-L extsuperscript{e}-Yomdin polynomials.

Findings

Constructed new $ppa$-Zariski pairs of surface singularities.

Established a method based on Newton weighted-L extsuperscript{e}-Yomdin polynomials.

Enhanced classification techniques for surface singularities.

Abstract

We investigate surface singularities defined by weighted-L\^e-Yomdin polynomials, with a particular focus on a specific subclass that we refer to as Newton weighted-L\^e-Yomdin polynomials. In particular, using polynomials in this subclass, we develop a method to construct new $\mu$-Zariski pairs of surface singularities.