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Modules de feuilletages holomorphes singuliers. I: équisingularité. (Modules of singular holomorphic foliations. I: Equisingularity). (French) Zbl 0709.32025

We prove that there exists a semi-universal unfolding in the equisingular unfolding class, for a germ in \(0\in ({\mathbb{C}}^ 2)\) of holomorphic singular foliation. We give an explicit formula for the dimension of the universal parameter space, with respect to multiplicities of the infinitely near points. This result applied to a function gives a formula for the dimension of the \(\mu\)-constant strata.
Reviewer: J.F.Mattei

MSC:

32S15 Equisingularity (topological and analytic)
32S65 Singularities of holomorphic vector fields and foliations
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