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arXiv · 2401.09397

Algebraic integrability with bounded genus

Carlos Galindo·Francisco Monserrat·Elvira Pérez-Callejo
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Abstract

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.

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Carlos Galindo, Francisco Monserrat, Elvira Pérez-Callejo. 2024-01-17. Algebraic integrability with bounded genus. https://doi.org/10.1016/j.jde.2025.113466

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