Moduli spaces for topologically quasi-homogeneous functions

Yohann Genzmer and Emmanuel Paul

Journal of Singularities
volume 14 (2016), 3-33

Received 29 April 2014. Received in revised form 29 September 2015.

DOI: 10.5427/jsing.2016.14b

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Abstract:

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 (df=0) and a germ of curve (f=0). We first describe the moduli space of the foliations in this class and we 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.

Keywords:

holomorphic foliation, moduli of curve, singularities

2010 Mathematical Subject Classification:

34M35, 32S65, 32G13

Author(s) information:

Yohann Genzmer	Emmanuel Paul
Institut de Mathématiques de Toulouse	Institut de Mathématiques de Toulouse
Université Paul Sabatier	Université Paul Sabatier
118 route de Narbonne	118 route de Narbonne
31062 Toulouse cedex 9, France	31062 Toulouse cedex 9, France
email: yohann.genzmer@math.univ-toulouse.fr	email: emmanuel.paul@math.univ-toulouse.fr