A Comprehensive Approach to the Moduli Space of Quasi-homogeneous Singularities

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 222)

Abstract

We study the relationship between singular holomorphic foliations at \((\mathbb {C}^{2},0)\) and their separatrices. Under mild conditions we describe a complete set of analytic invariants characterizing foliations with quasi-homogeneous separatrices. Further, we give the full moduli space of quasi-homogeneous plane curves. This paper has an expository character in order to make it accessible also to non-specialists.

Keywords

Singular holomorphic foliations Holonomy groups Quasi-homogeneous curves 

2010 Mathematics Subject Classification

37F75 32S65 32S45 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal do Espírito SantoVitória-ESBrazil
  2. 2.Intituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de Janeiro-RJBrazil

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