Modules de feuilletages holomorphes singuliers. I: équisingularité. (Modules of singular holomorphic foliations. I: Equisingularity) (Q921204)

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.