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

Abstract

In this work we use our previous results on the topological classification of generic singular foliation germs on ( C 2 , 0 ) (\mathbb {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.