The realization spaces of certain conic-line arrangements of degree 7

TL;DR

This paper investigates the topology of specific degree 7 conic-line arrangements, introduces new Zariski pairs, and computes their fundamental groups, enhancing understanding of their geometric and topological properties.

Contribution

It provides two new examples of Zariski pairs and determines the number of connected components for certain conic-line arrangements of degree 7.

Findings

Two new Zariski pairs identified

Number of connected components determined

Fundamental groups computed using SageMath

Abstract

We study the embedded topology of certain conic-line arrangements of degree 7. Two new examples of Zariski pairs are given. Furthermore, we determine the number of connected components of the conic-line arrangements. We also calculate the fundamental groups using SageMath and the package Sirocco in the appendix.