On the nearly freeness of conic-line arrangements with nodes, tacnodes, and ordinary triple points

Abstract

In the present note, we provide a partial classification of nearly free conic-line arrangements in the complex plane having nodes, tacnodes, and ordinary triple points. In this setting, our theoretical bound tells us that the degree of such an arrangement is bounded from above by 12. We construct examples of nearly free conic-line arrangements having degree 3, 4, 5, 6, 7, and we prove that in degree 10, 11, and 12, there is no such arrangement.