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Topological Moduli Space for Germs of Holomorphic Foliations III: Complete families (2201.07479v2)
Published 19 Jan 2022 in math.DS, math.CA, and math.CV
Abstract: 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.