Topological moduli space for germs of holomorphic foliations III: Complete families

In this work we use our previous results on the topological classification of generic singular foliation germs on (C 2, 0) (C^2, 0) to construct complete families: after fixing the semi-local topological invariants we prove the existence of a minimal family of foliation germs that contains all the topological classes and such that any equisingular global family with parameter space an arbitrary complex manifold factorizes through it.