On conic-line arrangements with nodes, tacnodes, and ordinary triple points

TL;DR

This paper investigates conic-line arrangements with specific singularities, establishing combinatorial constraints and providing a complete classification of free arrangements within this class.

Contribution

It introduces combinatorial constraints and offers the first complete classification of free conic-line arrangements with nodes, tacnodes, and triple points.

Findings

Derived combinatorial constraints for arrangements

Classified all free arrangements in this class

Enhanced understanding of singularity configurations

Abstract

In the present paper, we study conic-line arrangements having nodes, tacnodes, and ordinary triple points as singularities. We provide combinatorial constraints on such arrangements and we give the complete classification of free arrangements in this class.