A splitting theorem for the Kupka component of a foliation of $𝐂{𝐏}^n,n\ge 6$. Addendum to a paper by O. Calvo-Andrade and N. Soares

Ballico, Edoardo. "A splitting theorem for the Kupka component of a foliation of ${\bf C} {\bf P}^n,\,n\ge 6$. Addendum to a paper by O. Calvo-Andrade and N. Soares." Annales de l'institut Fourier 45.4 (1995): 1119-1121. <http://eudml.org/doc/75147>.

@article{Ballico1995,
abstract = {Here we show that a Kupka component $K$ of a codimension 1 singular foliation $F$ of $\{\bf C\}\{\bf P\}^n,\, n\ge 6$ with $\{\rm deg\}(K)$ not a square is a complete intersection. The result implies the existence of a meromorphic first integral of $F$.},
author = {Ballico, Edoardo},
journal = {Annales de l'institut Fourier},
keywords = {singular foliations; codimension 1 foliations; Kupka component; complete intersection; unstable vector bundle; rank 2 vector bundle; splitting of a vector bundle; meromorphic first integral; Barth-Lefschetz theorems},
language = {eng},
number = {4},
pages = {1119-1121},
publisher = {Association des Annales de l'Institut Fourier},
title = {A splitting theorem for the Kupka component of a foliation of $\{\bf C\} \{\bf P\}^n,\,n\ge 6$. Addendum to a paper by O. Calvo-Andrade and N. Soares},
url = {http://eudml.org/doc/75147},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Ballico, Edoardo
TI - A splitting theorem for the Kupka component of a foliation of ${\bf C} {\bf P}^n,\,n\ge 6$. Addendum to a paper by O. Calvo-Andrade and N. Soares
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 4
SP - 1119
EP - 1121
AB - Here we show that a Kupka component $K$ of a codimension 1 singular foliation $F$ of ${\bf C}{\bf P}^n,\, n\ge 6$ with ${\rm deg}(K)$ not a square is a complete intersection. The result implies the existence of a meromorphic first integral of $F$.
LA - eng
KW - singular foliations; codimension 1 foliations; Kupka component; complete intersection; unstable vector bundle; rank 2 vector bundle; splitting of a vector bundle; meromorphic first integral; Barth-Lefschetz theorems
UR - http://eudml.org/doc/75147
ER -