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

Ballico, Edoardo. "A splitting theorem for the Kupka component of a foliation of ${\mathbb {C}}{\mathbb {P}}^n,\;n\ge 6$. Addendum to an addendum to a paper by Calvo-Andrade and Soares." Annales de l'institut Fourier 49.4 (1999): 1423-1425. <http://eudml.org/doc/75387>.

@article{Ballico1999,
abstract = {Here we show that a Kupka component $K$ of a codimension 1 singular foliation $F$ of $\{\Bbb C\}\{\Bbb P\}^n,\;n\ge 6$ is a complete intersection. The result implies the existence of a meromorphic first integral of $F$. The result was previously known if $\{\rm deg\}(K)$ was assumed to be not a square.},
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 = {1423-1425},
publisher = {Association des Annales de l'Institut Fourier},
title = {A splitting theorem for the Kupka component of a foliation of $\{\mathbb \{C\}\}\{\mathbb \{P\}\}^n,\;n\ge 6$. Addendum to an addendum to a paper by Calvo-Andrade and Soares},
url = {http://eudml.org/doc/75387},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Ballico, Edoardo
TI - A splitting theorem for the Kupka component of a foliation of ${\mathbb {C}}{\mathbb {P}}^n,\;n\ge 6$. Addendum to an addendum to a paper by Calvo-Andrade and Soares
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 4
SP - 1423
EP - 1425
AB - Here we show that a Kupka component $K$ of a codimension 1 singular foliation $F$ of ${\Bbb C}{\Bbb P}^n,\;n\ge 6$ is a complete intersection. The result implies the existence of a meromorphic first integral of $F$. The result was previously known if ${\rm deg}(K)$ was assumed to be not a square.
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/75387
ER -