Algebraic integrability with bounded genus
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913939313393664 |
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| author | Galindo, Carlos Monserrat, Francisco Pérez-Callejo, Elvira |
| author_facet | Galindo, Carlos Monserrat, Francisco Pérez-Callejo, Elvira |
| contents | We provide an algorithm which decides whether a polynomial foliation $\mathcal{F}^{\mathbb{C}^2}$ on the complex plane has a polynomial first integral of genus $g\neq 1$. Except in a specific case, an extension of the algorithm also decides if $\mathcal{F}^{\mathbb{C}^2}$ has a rational first integral of that genus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09397 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic integrability with bounded genus Galindo, Carlos Monserrat, Francisco Pérez-Callejo, Elvira Algebraic Geometry Dynamical Systems We provide an algorithm which decides whether a polynomial foliation $\mathcal{F}^{\mathbb{C}^2}$ on the complex plane has a polynomial first integral of genus $g\neq 1$. Except in a specific case, an extension of the algorithm also decides if $\mathcal{F}^{\mathbb{C}^2}$ has a rational first integral of that genus. |
| title | Algebraic integrability with bounded genus |
| topic | Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2401.09397 |