Algebraic integrability with bounded genus

2024/01/17 by Carlos Galindo, Galindo, Carlos, Francisco Monserrat +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2401.09397

openalex publication_date 2024/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an algorithm which decides whether a polynomial foliation F^ℂ2 on the complex plane has a polynomial first integral of genus g≠ 1. Except in a specific case, an extension of the algorithm also decides if F^ℂ2 has a rational first integral of that genus.

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