Moduli spaces of germs of holomorphic foliations in the plane
Tóm tắt
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.