Here we show that a Kupka component of a codimension 1 singular foliation of is a complete intersection. The result implies the existence of a meromorphic first integral of . The result was previously known if was assumed to be not a square.
On considère ici les feuilletages holomorphes singuliers de codimension 1 dans avec une composante de Kupka compacte . On démontre que est une intersection complète.
@article{AIF_1999__49_4_1423_0, author = {Ballico, Edoardo}, 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}}, journal = {Annales de l'Institut Fourier}, pages = {1423--1425}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {49}, number = {4}, year = {1999}, doi = {10.5802/aif.1723}, zbl = {0959.32037}, mrnumber = {2001b:32059}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1723/} }
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 SP - 1423 EP - 1425 VL - 49 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1723/ DO - 10.5802/aif.1723 LA - en ID - AIF_1999__49_4_1423_0 ER -
%0 Journal Article %A Ballico, Edoardo %T 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 %J Annales de l'Institut Fourier %D 1999 %P 1423-1425 %V 49 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1723/ %R 10.5802/aif.1723 %G en %F AIF_1999__49_4_1423_0
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, Volume 49 (1999) no. 4, pp. 1423-1425. doi : 10.5802/aif.1723. https://aif.centre-mersenne.org/articles/10.5802/aif.1723/
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