Non-algebraicity of foliations via reduction modulo $2$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915380663943168 |
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| author | Figueredo, João Paulo Mendson, Wodson |
| author_facet | Figueredo, João Paulo Mendson, Wodson |
| contents | Motivated by the Jouanolou foliation problem, we investigate the non-algebraicity of foliations by curves on $\mathbb{P}^2_{\mathbb{C}}$. We present a criterion to show that such a foliation has no algebraic invariant curves, using a method of reduction modulo $2$. Finally, using this criterion, we give a new proof that the Jouanolou foliation of odd degree has no algebraic invariant curves. We also present other classes of foliations without algebraic invariant curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-algebraicity of foliations via reduction modulo $2$ Figueredo, João Paulo Mendson, Wodson Algebraic Geometry 32S65, 13N15, 13A35 Motivated by the Jouanolou foliation problem, we investigate the non-algebraicity of foliations by curves on $\mathbb{P}^2_{\mathbb{C}}$. We present a criterion to show that such a foliation has no algebraic invariant curves, using a method of reduction modulo $2$. Finally, using this criterion, we give a new proof that the Jouanolou foliation of odd degree has no algebraic invariant curves. We also present other classes of foliations without algebraic invariant curves. |
| title | Non-algebraicity of foliations via reduction modulo $2$ |
| topic | Algebraic Geometry 32S65, 13N15, 13A35 |
| url | https://arxiv.org/abs/2507.07277 |