Dicritical nilpotent holomorphic foliations

Percy Fernández-Sánchez; Jorge Mozo-Fernández; Hernán Neciosup

doi:10.3934/dcds.2018140

Dicritical nilpotent holomorphic foliations

Percy Fernández-Sánchez
, Jorge Mozo-Fernández
, Hernán Neciosup

Grupo de investigación en Geometría y Dinámica Compleja

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

1 Cita (Scopus)

Resumen

We study in this paper several properties concerning singularities of foliations in (C³, 0) that are pull-back of dicritical foliations in (C², 0). Particularly, we will investigate the existence of first integrals (holomorphic and meromorphic) and the dicriticalness of such a foliation. In the study of meromorphic first integrals we follow the same method used by R. Meziani and P. Sad in dimension two. While the foliations we study are pull-back of foliations in (C², 0), the adaptations are not straightforward.

Idioma original	Inglés
Páginas (desde-hasta)	3223-3237
Número de páginas	15
Publicación	Discrete and Continuous Dynamical Systems- Series A
Volumen	38
N.º	7
DOI	https://doi.org/10.3934/dcds.2018140
Estado	Publicada - jul. 2018

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title = "Dicritical nilpotent holomorphic foliations",

abstract = "We study in this paper several properties concerning singularities of foliations in (C3, 0) that are pull-back of dicritical foliations in (C2, 0). Particularly, we will investigate the existence of first integrals (holomorphic and meromorphic) and the dicriticalness of such a foliation. In the study of meromorphic first integrals we follow the same method used by R. Meziani and P. Sad in dimension two. While the foliations we study are pull-back of foliations in (C2, 0), the adaptations are not straightforward.",

keywords = "Holomorphic foliations, dicritical foliations.",

author = "Percy Fern{\'a}ndez-S{\'a}nchez and Jorge Mozo-Fern{\'a}ndez and Hern{\'a}n Neciosup",

year = "2018",

month = jul,

doi = "10.3934/dcds.2018140",

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AU - Mozo-Fernández, Jorge

AU - Neciosup, Hernán

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N2 - We study in this paper several properties concerning singularities of foliations in (C3, 0) that are pull-back of dicritical foliations in (C2, 0). Particularly, we will investigate the existence of first integrals (holomorphic and meromorphic) and the dicriticalness of such a foliation. In the study of meromorphic first integrals we follow the same method used by R. Meziani and P. Sad in dimension two. While the foliations we study are pull-back of foliations in (C2, 0), the adaptations are not straightforward.

AB - We study in this paper several properties concerning singularities of foliations in (C3, 0) that are pull-back of dicritical foliations in (C2, 0). Particularly, we will investigate the existence of first integrals (holomorphic and meromorphic) and the dicriticalness of such a foliation. In the study of meromorphic first integrals we follow the same method used by R. Meziani and P. Sad in dimension two. While the foliations we study are pull-back of foliations in (C2, 0), the adaptations are not straightforward.

KW - Holomorphic foliations, dicritical foliations.

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 7

ER -

Dicritical nilpotent holomorphic foliations

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