Construction of free curves by adding osculating conics to a given cubic curve
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| author | Dimca, Alexandru Ilardi, Giovanna Malara, Grzegorz Pokora, Piotr |
| author_facet | Dimca, Alexandru Ilardi, Giovanna Malara, Grzegorz Pokora, Piotr |
| contents | In the present article we construct new families of free and nearly free curves starting from a plane cubic curve $C$ 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 $27$ hyperosculating conics of the Fermat cubic curve using well-chosen group actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08913 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Construction of free curves by adding osculating conics to a given cubic curve Dimca, Alexandru Ilardi, Giovanna Malara, Grzegorz Pokora, Piotr Algebraic Geometry Commutative Algebra Combinatorics 14C20, 14N20, 32S22 In the present article we construct new families of free and nearly free curves starting from a plane cubic curve $C$ 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 $27$ hyperosculating conics of the Fermat cubic curve using well-chosen group actions. |
| title | Construction of free curves by adding osculating conics to a given cubic curve |
| topic | Algebraic Geometry Commutative Algebra Combinatorics 14C20, 14N20, 32S22 |
| url | https://arxiv.org/abs/2311.08913 |