English

Addition-deletion results for plus-one generated curves

Algebraic Geometry 2024-11-12 v4 Commutative Algebra

Abstract

In the recent paper A. Dimca proves that when one adds to or deletes a line from a free curve the resulting curve is either free or plus-one generated. We prove the converse statements, we give an additional insight into the original deletion result, and derive a characterisation of free curves in terms of behaviour to addition/deletion of lines. We describe the possible splitting types of the bundle of logarithmic vector fields associated to a plus-one generated curve.

Cite

@article{arxiv.2310.19610,
  title  = {Addition-deletion results for plus-one generated curves},
  author = {Anca Măcinic and Piotr Pokora},
  journal= {arXiv preprint arXiv:2310.19610},
  year   = {2024}
}

Comments

Minor changes

R2 v1 2026-06-28T13:06:01.059Z