Construction of free curves by adding osculating conics to a given cubic curve
Algebraic Geometry
2025-02-17 v2 Commutative Algebra
Combinatorics
Abstract
In the present article we construct new families of free and nearly free curves starting from a plane cubic curve and adding some of its hyperosculating conics. We present results that involve nodal cubic curves and the Fermat cubic. In addition, we provide new insight into the geometry of the hyperosculating conics of the Fermat cubic curve using well-chosen group actions.
Cite
@article{arxiv.2311.08913,
title = {Construction of free curves by adding osculating conics to a given cubic curve},
author = {Alexandru Dimca and Giovanna Ilardi and Grzegorz Malara and Piotr Pokora},
journal= {arXiv preprint arXiv:2311.08913},
year = {2025}
}
Comments
14 pages, final version incorporating referee's remarks, to appear in International Mathematical Research Notes