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arXiv · 2105.12688

Topological moduli space for germs of holomorphic foliations II: Universal deformations

David Marín·Jean-François Mattei·Éliane Salem
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Abstract

This work deals with the topological classification of singular foliation germs on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and the projective holonomy representations and we prove the existence of a topological universal deformation through which every equisingular deformation uniquely factorizes up to topological conjugacy. This is done by representing the functor of topological classes of equisingular deformations of a fixed foliation. We also describe the functorial dependence of this representation with respect to the foliation.

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BibTeXRIS

David Marín, Jean-François Mattei, Éliane Salem. 2021-05-26. Topological moduli space for germs of holomorphic foliations II: Universal deformations. https://arxiv.org/abs/2105.12688

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