New $\mu$-Zariski pairs of surface singularities

TL;DR

This paper introduces a new example of a $$-Zariski pair of surface singularities in complex three-space, expanding beyond previously known L-Yomdin types.

Contribution

The authors present the first known $$-Zariski pair involving surface singularities that are not of L-Yomdin type, broadening the scope of known examples.

Findings

First example of a $$-Zariski pair outside L-Yomdin singularities

Expands understanding of surface singularity classifications

Provides new insights into the topology of complex surface singularities

Abstract

To the best of the authors' knowledge, all previously known examples of $\mu$-, $\mu^*$-, link-, or ordinary Zariski pairs of surface singularities in $\mathbb{C}^3$ consist of (possibly weighted) L\^e-Yomdin singularities. In this paper, we present an example of a $\mu$-Zariski pair involving surface singularities that are not of L\^e-Yomdin type.