The Hesse pencil of plane curves and osculating conics
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916780973228032 |
|---|---|
| author | Nawara, Ewelina |
| author_facet | Nawara, Ewelina |
| contents | In this paper, we revisit the classical problem of determining osculating conics and sextactic points for a given algebraic curve. Our focus is on a particular family of plane cubic curves known as the Hesse pencil. By employing classical tools from projective differential geometry, we derive explicit coordinates for these special points. The resulting formulas not only clarify previous approaches but also lead to the construction of new families of free and nearly free curves, extending recent findings the freeness of curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Hesse pencil of plane curves and osculating conics Nawara, Ewelina Algebraic Geometry 14H50, 53A15, 14N05 In this paper, we revisit the classical problem of determining osculating conics and sextactic points for a given algebraic curve. Our focus is on a particular family of plane cubic curves known as the Hesse pencil. By employing classical tools from projective differential geometry, we derive explicit coordinates for these special points. The resulting formulas not only clarify previous approaches but also lead to the construction of new families of free and nearly free curves, extending recent findings the freeness of curves. |
| title | The Hesse pencil of plane curves and osculating conics |
| topic | Algebraic Geometry 14H50, 53A15, 14N05 |
| url | https://arxiv.org/abs/2506.04662 |