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

Pontifical Catholic Univ. of Peru
University of Valladolid

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	3223-3237
Number of pages	15
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	38
Issue number	7
DOIs	https://doi.org/10.3934/dcds.2018140
State	Published - Jul 2018

Keywords

Holomorphic foliations, dicritical foliations.

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10.3934/dcds.2018140

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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.",

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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.

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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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Keywords

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