Zariski pairs of conic-line arrangements with a unique conic

TL;DR

This paper constructs two examples of conic-line arrangements with a single conic that are topologically distinct yet share the same combinatorial structure, illustrating Zariski pairs in degree 9.

Contribution

It introduces specific Zariski pairs of conic-line arrangements with a unique conic, distinguished by their topological properties using connected numbers.

Findings

Two Zariski pairs of degree 9 conic-line arrangements with a unique conic.

Topological differences are detected via connected numbers.

Demonstrates the existence of Zariski pairs in this class of arrangements.

Abstract

In this note, we present two pairs of conic-line arrangements admitting a unique conic and that form Zariski pairs, both of degree $9$. Their topologies are distinguished using the connected numbers.