Deletion-addition of a smooth conic for free curves

Abstract

We describe the behaviour of a free reduced plane projective curve with respect to the deletion, respectively addition, of a smooth conic. These results apply in particular to conic-line arrangements. We present some obstructions to the geometry and combinatorics of a free reduced curve, generalizing results known a priori only for free projective line arrangements.

Clarified some notations. Added Corollaries 3.15, 3.17

References in corpus (5)

• $\mathcal{Q}$-conic arrangements in the complex projective plane
• On plus-one generated conic-line arrangements with simple singularities
• Addition-deletion results for plus-one generated curves
• Construction of free curves by adding osculating conics to a given cubic curve
• A geometric perspective on plus-one generated arrangements of lines