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.
Original language | English |
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Pages (from-to) | 518-539 |
Journal | Commentarii Mathematici Helvetici |
Volume | 78 |
DOIs | |
Publication status | Published - 1 Sep 2003 |
Keywords
- Holomorphic foliation
- Holonomy representation
- Moduli space