English

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