Differentiable equisingularity of holomorphic foliations

We prove that a \(C^{\infty}\) equivalence between germs holomorphic foliations at \(({\mathbb C}^2,0)\) 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 equi...

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Bibliographic Details
Published in:arXiv.org 2016-11
Main Authors: Mol, Rogério, Rosas, Rudy
Format: Article
Language:English
Subjects:
Mathematical analysis
Online Access:Get full text
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Summary:We prove that a \(C^{\infty}\) equivalence between germs holomorphic foliations at \(({\mathbb C}^2,0)\) 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.
ISSN:2331-8422