Abstract
In this paper we study the topological moduli space of some germs of singular holomorphic foliations in (ℂ2,0). We obtain a fully characterization for generic foliations whose vanishing order at the origin is two or three. We give a similar description for a certain subspace in the moduli space of generic germs of homogeneous foliations of any vanishing order and also for generic quasi-homogeneous foliations. In all the cases we identify the fundamental group of these spaces using the Gassner representation of the pure braid group and a suitable holonomy representation of the foliation.
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Marín, D. Moduli spaces of germs of holomorphic foliations in the plane . Comment. Math. Helv. 78, 518–539 (2003). https://doi.org/10.1007/s00014-003-0771-z
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DOI: https://doi.org/10.1007/s00014-003-0771-z