Moduli spaces of germs of holomorphic foliations in the plane

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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 languageEnglish
Pages (from-to)518-539
JournalCommentarii Mathematici Helvetici
Volume78
DOIs
Publication statusPublished - 1 Sep 2003

Keywords

  • Holomorphic foliation
  • Holonomy representation
  • Moduli space

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