Moduli spaces of germs of holomorphic foliations in the plane

David Maŕin

doi:https://doi.org/10.1007/s00014-003-0771-z

Moduli spaces of germs of holomorphic foliations in the plane

David Maŕin

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

11 Citations (Scopus)

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
Pages (from-to)	518-539
Journal	Commentarii Mathematici Helvetici
Volume	78
DOIs	https://doi.org/10.1007/s00014-003-0771-z
Publication status	Published - 1 Sep 2003

Keywords

Holomorphic foliation
Holonomy representation
Moduli space

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AB - 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.

KW - Holomorphic foliation

KW - Holonomy representation

KW - Moduli space

U2 - https://doi.org/10.1007/s00014-003-0771-z

DO - https://doi.org/10.1007/s00014-003-0771-z

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