On non-Kupka points of codimension one foliations on ℙ3

Omegar Calvo-Andrade; Maurício Côrrea; Arturo Fernández-Pérez

doi:10.1590/0001-3765201620160013

On non-Kupka points of codimension one foliations on ℙ3

An Acad Bras Cienc. 2016 Oct-Dec;88(4):2067-2080. doi: 10.1590/0001-3765201620160013.

Authors

Omegar Calvo-Andrade¹, Maurício Côrrea², Arturo Fernández-Pérez²

Affiliations

¹ Centro de Investigaciones en Matemáticas/CIMAT, A.C., Jalisco, s/n, Col. Valenciana CP 36023 Guanajuato, Gto, México.
² Universidade Federal de Minas Gerais, Departamento de Matemática, Av. Antônio Carlos, 6627, 31270-901 Belo Horizonte, MG, Brazil.

PMID: 27991951
DOI: 10.1590/0001-3765201620160013

Abstract

We study the singular set of a codimension one holomorphic foliation on ℙ 3 . We find a local normal form for these foliations near a codimension two component of the singular set that is not of Kupka type. We also determine the number of non-Kupka points immersed in a codimension two component of the singular set of a codimension one foliation on ℙ 3.