On the topology of the complements of reducible plane curves via Galois covers

TL;DR

This paper explores the topology of reducible plane curve complements using Galois covers and Alexander polynomials, providing new insights and examples of Zariski N-plets for conic configurations.

Contribution

It introduces a novel approach combining Galois covers and Alexander polynomials to analyze the topology of reducible plane curves.

Findings

Effective in distinguishing Zariski N-plets

Provides new examples for conic and quartic configurations

Enhances understanding of plane curve topology

Abstract

Let ${\mathcal {B}}$ be a reducible reduced plane curve. We introduce a new point of view to study the topology of $(\PP^2, {\mathcal {B}})$ via Galois covers and Alexander polynomials. We show its effectiveness through examples of Zariski $N$-plets for conic and conic-quartic configurations.