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.
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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 |