Moduli spaces for topologically quasi-homogeneous functions.

Yohann Genzmer (1) , Emmanuel Paul (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider the topological class of a germ of 2-variables quasi-homogeneous complex analytic function. Each element f in this class induces a germ of foliation (f = constants) and a germ of curve (f = 0). We first describe the moduli space of the foliations in this class and give analytic normal forms. The classification of curves induces a distribution on this moduli space. By studying the infinitesimal generators of this distribution, we can compute the generic dimension of the moduli space for the curves, and we obtain the corresponding generic normal forms.

Domaines: Variables complexes [math.CV]; Systèmes dynamiques [math.DS]

Yohann Genzmer, Emmanuel Paul. Moduli spaces for topologically quasi-homogeneous functions.. Journal of Singularities, 2016. ⟨hal-00749661⟩