Moduli spaces of germs of holomorphic foliations in the plane

• Autores: David Marín Pérez
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 78, Nº 3, 2003, págs. 518-539
• Idioma: inglés
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• Resumen

  • 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 Gassner representation of the pure braid group and a suitable holonomy representation of the foliation