Deletion-addition of a smooth conic for free curves
Algebraic Geometry
2026-03-25 v6 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.2408.11714,
title = {Deletion-addition of a smooth conic for free curves},
author = {Anca Macinic},
journal= {arXiv preprint arXiv:2408.11714},
year = {2026}
}
Comments
Clarified some notations. Added Corollaries 3.15, 3.17