Differentiable equisingularity of holomorphic foliations

Rogério Mol; Rudy Rosas

doi:10.5427/jsing.2019.19f

Differentiable equisingularity of holomorphic foliations

Rogério Mol
, Rudy Rosas

Sección de Matemáticas

Universidade Federal de Minas Gerais

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

4 Citas (Scopus)

Resumen

We prove that a C^∞ equivalence between germs of holomorphic foliations at (C², 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.

Idioma original	Inglés
Páginas (desde-hasta)	76-96
Número de páginas	21
Publicación	Journal of Singularities
Volumen	19
DOI	https://doi.org/10.5427/jsing.2019.19f
Estado	Publicada - 2019

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title = "Differentiable equisingularity of holomorphic foliations",

abstract = "We prove that a C∞ equivalence between germs of holomorphic foliations at (C2, 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 = "Equidesingularization, Holomorphic foliations, Invariant curves, Vector ﬁelds",

author = "Rog{\'e}rio Mol and Rudy Rosas",

year = "2019",

doi = "10.5427/jsing.2019.19f",

language = "English",

volume = "19",

pages = "76--96",

journal = "Journal of Singularities",

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TY - JOUR

T1 - Differentiable equisingularity of holomorphic foliations

AU - Mol, Rogério

AU - Rosas, Rudy

PY - 2019

Y1 - 2019

N2 - We prove that a C∞ equivalence between germs of holomorphic foliations at (C2, 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.

AB - We prove that a C∞ equivalence between germs of holomorphic foliations at (C2, 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.

KW - Equidesingularization

KW - Holomorphic foliations

KW - Invariant curves

KW - Vector ﬁelds

UR - https://www.scopus.com/pages/publications/85073273862

U2 - 10.5427/jsing.2019.19f

DO - 10.5427/jsing.2019.19f

M3 - Article

AN - SCOPUS:85073273862

SN - 1949-2006

VL - 19

SP - 76

EP - 96

JO - Journal of Singularities

JF - Journal of Singularities

ER -

Differentiable equisingularity of holomorphic foliations

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