Platitude des tissus duaux de certains pré-feuilletages convexes du plan projectif complexe

2024/05/08 by Samir Bedrouni, Bedrouni, Samir
Mathematics · #14C21 #32S65 #53A60 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2405.05464

openalex publication_date 2024/05/08 · openalex created_date 2024/05/11 · openalex updated_date 2026/07/28

Abstract

A holomorphic pre-foliation \mathscrF=C\boxtimesF on ℙ²_ℂ is the data of a reduced complex projective curve C of ℙ²_ℂ and a holomorphic foliation F on ℙ²_ℂ. When the foliation F is convex and the curve C is invariant by F, we speak of convex pre-foliation. In a previous paper, we showed that if a foliation F on ℙ²_ℂ is reduced convex or homogeneous convex and if C is an invariant line of F, then the dual web of the convex pre-foliation C\boxtimesF is flat. In this paper, we propose to extend this result to the case of a curve C consisting of several invariant lines.

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