On mutual arrangements of a plane real curve relative to an $M$-quartic with an oval-snake
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908697474629632 |
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| author | Orevkov, S. Yu. Puchkova, N. D. |
| author_facet | Orevkov, S. Yu. Puchkova, N. D. |
| contents | An oval $O$ of a plane real algebraic quartic curve $S$ is called a snake coiling around a real curve $C_k$ of degree $k$ if $O\cup\mathbb{R}C_k$ is isotopic to $O'\cup\mathbb{R}C_k$, where $O'$ is the boundary of a thickening of the embedded segment that transversally intersects $\mathbb{R}C_k$ at $2k$ points. In this article we prove that in this case $\mathbb{R}C_k\cup\mathbb{R}S$ is isotopic to $\mathbb{R}C_k\cup\mathbb{R}Q$, where $Q$ is a perturbation of the doubled conic. We prove analogs of this statement for real pseudoholomorphic curves under some additional assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On mutual arrangements of a plane real curve relative to an $M$-quartic with an oval-snake Orevkov, S. Yu. Puchkova, N. D. Algebraic Geometry An oval $O$ of a plane real algebraic quartic curve $S$ is called a snake coiling around a real curve $C_k$ of degree $k$ if $O\cup\mathbb{R}C_k$ is isotopic to $O'\cup\mathbb{R}C_k$, where $O'$ is the boundary of a thickening of the embedded segment that transversally intersects $\mathbb{R}C_k$ at $2k$ points. In this article we prove that in this case $\mathbb{R}C_k\cup\mathbb{R}S$ is isotopic to $\mathbb{R}C_k\cup\mathbb{R}Q$, where $Q$ is a perturbation of the doubled conic. We prove analogs of this statement for real pseudoholomorphic curves under some additional assumptions. |
| title | On mutual arrangements of a plane real curve relative to an $M$-quartic with an oval-snake |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.06907 |