Non-algebraicity of foliations via reduction modulo $2$

João Paulo Figueredo; Wodson Mendson

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arXiv · 2507.07277

Non-algebraicity of foliations via reduction modulo $2$

João Paulo Figueredo·Wodson Mendson

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Abstract

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.

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BibTeX RIS

João Paulo Figueredo, Wodson Mendson. 2025-07-09. Non-algebraicity of foliations via reduction modulo $2$. https://arxiv.org/abs/2507.07277

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