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