Moduli spaces of germs of holomorphic foliations in the plane

David Mar�n
2003 Commentarii Mathematici Helvetici  
In this paper we study the topological moduli space of some germs of singular holomorphic foliations in (C 2 , 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
more » ... representation of the pure braid group and a suitable holonomy representation of the foliation.
doi:10.1007/s00014-003-0771-z fatcat:btwwtrzjdfgrhch6gkspoem634