Analytical and formal classifications of quasi-homogeneous foliations in (C²,0)

2007/01/08 by Yohann Genzmer, Y. Genzmer, Genzmer, Y. · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DS

paper · pdf · doi:10.48550/arxiv.math/0701220

arxiv created 2007/01/08 · openalex publication_date 2007/01/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a result of classification for germs of formal and convergent quasi-homogeneous foliations in C² with fixed separatrix. Basically, we prove that the analytical and formal class of such a foliation depend respectively only on the analytical and formal class of its representation of projective holonomy.

Citations

• Modules formels locaux de feuilletages holomorphes

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• On some indices of foliations and applications

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