Moduli spaces of a family of topologically non quasi-homogeneous functions

2018/10/31 by Jinan Loubani, Loubani, Jinan
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.1810.13176

openalex publication_date 2018/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a topological class of a germ of complex analytic function in two variables which does not belong to its jacobian ideal. Such a function is not quasi homogeneous. Each element f in this class induces a germ of foliation (df = 0). Proceeding similarly to the homogeneous case and the quasi homogeneous case treated by Genzmer and Paul, we describe the local moduli space of the foliations in this class and give analytic normal forms. We prove also the uniqueness of these normal forms.

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