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) 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.