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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.
Marín et al. (Fri,) studied this question.