no. 4
A splitting theorem for the Kupka component of a foliation of ℂℙ n ,n≥6. Addendum to an addendum to a paper by Calvo-Andrade and Soares
Annales de l'Institut Fourier, Tome 49 (1999) no. 4, pp. 1423-1425.

On considère ici les feuilletages holomorphes singuliers de codimension 1 dans ℂℙ n ,n≥6 avec une composante de Kupka compacte K. On démontre que K est une intersection complète.

Here we show that a Kupka component K of a codimension 1 singular foliation F of ℂℙ n ,n≥6 is a complete intersection. The result implies the existence of a meromorphic first integral of F. The result was previously known if deg (K) was assumed to be not a square.

@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},
     mrnumber = {2001b:32059},
     zbl = {0959.32037},
     language = {en},
     url = {http://archive.numdam.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  - http://archive.numdam.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 http://archive.numdam.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, Tome 49 (1999) no. 4, pp. 1423-1425. doi : 10.5802/aif.1723. http://archive.numdam.org/articles/10.5802/aif.1723/

[B] E. Ballico, A splitting theorem for the Kupka component of a foliation of ℂℙn, n ≥ 6. Addendum to a paper by Calvo-Andrade and Soares, Ann. Inst. Fourier, 45-4 (1995), 1119-1121. | Numdam | Zbl

[CS] O. Calvo-Andrade, M. Soares, Chern numbers of a Kupka component, Ann. Inst. Fourier, 44-4 (1994), 1219-1236. | Numdam | MR | Zbl

[CL] D. Cerveau, A. Lins, Codimension one foliations in ℂℙn n ≥ 3, with Kupka components, in Complex analytic methods in dinamical systems, Astérisque, (1994), 93-133. | Zbl

[F] G. Faltings, Ein Kriterium für vollständige Durchsnitte, Invent. Math., 62 (1981), 393-401. | MR | Zbl

[FL] W. Fulton, R. Lazarsfeld, Connectivity in algebraic geometry, in Algebraic Geometry, Proceedings Chicago 1980, Lect. Notes in Math. 862, Springer-Verlag (1981), 26-92. | MR | Zbl

[GN] X. Gomez-Mont, A. Lins-Neto, A structural stability of foliations with a meromorphic firs integral, Topology, 30 (1990), 315-334. | MR | Zbl

[GH] Ph. Griffiths, J. Harris, Principles of Algebraic Geometry, John Wiley & Sons, 1978. | Zbl

[OSS] Ch. Okonek, M. Schneider, H. Spindler, Vector Bundles on Complex Projective spaces, Progress in Math., 3, Birkhäuser, Basel, 1978.

Cité par Sources :