Differentiable equisingularity of holomorphic foliations

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: