Differentiable equisingularity of holomorphic foliations

Rogério Mol and Rudy Rosas

Journal of Singularities
volume 19 (2019), 76-96

Received: 10 October 2018. Accepted: 18 July 2019.

DOI: 10.5427/jsing.2019.19f

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Abstract:

We prove that a smooth equivalence between germs of holomorphic foliations at (C^2,0) establishes a bijection between the sets of formal separatrices preserving equisingularity classes. As a consequence, if one of the foliations is of second type, so is the other and they are equisingular.


Keywords:

holomorphic foliations, vector fields, invariant curves, equidesingularization


Mathematical Subject Classification (2010):

32S65, 37F75


Author(s) information:

Rogério Mol Rudy Rosas
Departamento de Matemática Pontificia Universidad Católica del Perú
Universidade Federal de Minas Gerais Av. Universitaria 1801
Av. Antônio Carlos, 6627 Lima, Peru
C.P. 702, 30123-970, Belo Horizonte, MG, Brasil
email: rmol@ufmg.br email: rudy.rosas@pucp.edu.pe