Differentiable equisingularity of holomorphic foliations

Rogério Mol, Rudy Rosas

Type: Article

Publication Date: 2019-01-01

Citations: 1

DOI: https://doi.org/10.5427/jsing.2019.19f

Abstract

We prove that a C ∞ equivalence between germs 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.

Locations

arXiv (Cornell University) - View - PDF
Journal of Singularities - View

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+ PDF Chat	Separatrices for Real Analytic Vector Fields in the Plane	2022	Eduardo Cabrera Rogério Mol

Works Cited by This (9)

Action	Title	Year	Authors
+ PDF Chat	Topological invariants and equidesingularization for holomorphic vector fields	1984	César Camacho Alcides Lins Neto Paulo Sad
+	Modules formels locaux de feuilletages holomorphes	2004	Jean-François Mattéi Éliane Salem
+	Local polar invariants for plane singular foliations	2015	Felipe Cano Nuria Corral Rogério Mol
+ PDF Chat	Meromorphic first integrals: some extension results	2002	Rogério Mol
+	On the Topology of Algebroid Singularities	1932	Oscar Zariski
+ PDF Chat	The C^1 invariance of the algebraic multiplicity of a holomorphic vector field	2010	Rudy Rosas
+ PDF Chat	The differentiable-invariance of the algebraic multiplicity of a holomorphic vector field	2009	Rudy Rosas
+	Reduction of singularities of the differential equation A dy=B dx	1979	Arno van den Essen
+	Local polar invariants for plane singular foliations	2015	Felipe Cano Nuria Corral Rogério Mol