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

Marín, David; Mattei, Jean-François; Salem, Eliane

doi:10.1090/tran/9250

Topological moduli space for germs of holomorphic foliations III: Complete families
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by David Marín, Jean-François Mattei and Eliane Salem;

Trans. Amer. Math. Soc. 377 (2024), 7309-7335

DOI: https://doi.org/10.1090/tran/9250

Published electronically: August 16, 2024

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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 contains all the topological classes and such that any equisingular global family with parameter space an arbitrary complex manifold factorizes through it.

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