Work

Arithmetic aspects of the Jouanolou foliation

Year: 2025

Type: article

Abstract: We investigate the structure of the [Formula: see text]-divisor associated with the Jouanolou foliation and we show, under certain conditions, that it can be irreducible or have a [Formula: see text]-factor. Furthermore, we study the reduction modulo [Formula: see text] of foliations and explore its applications to problems involving holomorphic foliations. As an application, we provide a new proof, via reduction modulo 2, of the fact that the Jouanolou foliation on the complex projective plane of odd degree, under specific arithmetic conditions, has no algebraic invariant curves.

Source: Journal of Algebra and Its Applications

DOI: 10.1142/s021949882650218x

Author: Wodson Mendson

Institutions: Institut de recherche mathématique de Rennes, Université Rennes 1, Université de Rennes

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

OpenAlex ID: W4409972933

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