Contact Invariants for Plane Curves in a Pencil
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910263755669504 |
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| author | Ciliberto, Ciro Miranda, Rick Roe, Joaquim |
| author_facet | Ciliberto, Ciro Miranda, Rick Roe, Joaquim |
| contents | Let $\calP$ be a general pencil of curves of degree $d$ in the projective plane. In this paper we review the computation of the number of curves in $\calP$ that have a hyperflex line, a flex bitangent line or a tritangent line. Then we focus on the curves in the dual plane described by the flex tangents and the bitangents of the curves of $\calP$ and the curves in the original plane described by the flexes and the points of bitangencies of the curves in $\calP$. Some of these curves have been studied already: we mainly focus here on the ones that still have not been treated systematically, and we compute their degree, genus, and singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27623 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contact Invariants for Plane Curves in a Pencil Ciliberto, Ciro Miranda, Rick Roe, Joaquim Algebraic Geometry 14H50, 14N05, 14N10 Let $\calP$ be a general pencil of curves of degree $d$ in the projective plane. In this paper we review the computation of the number of curves in $\calP$ that have a hyperflex line, a flex bitangent line or a tritangent line. Then we focus on the curves in the dual plane described by the flex tangents and the bitangents of the curves of $\calP$ and the curves in the original plane described by the flexes and the points of bitangencies of the curves in $\calP$. Some of these curves have been studied already: we mainly focus here on the ones that still have not been treated systematically, and we compute their degree, genus, and singularities. |
| title | Contact Invariants for Plane Curves in a Pencil |
| topic | Algebraic Geometry 14H50, 14N05, 14N10 |
| url | https://arxiv.org/abs/2605.27623 |