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

Ballico, Edoardo

doi:10.5802/aif.1487

A splitting theorem for the Kupka component of a foliation of

𝐂 𝐏^{n}, n \geq 6

. Addendum to a paper by O. Calvo-Andrade and N. Soares

Ballico, Edoardo

Annales de l'Institut Fourier, Tome 45 (1995) no. 4, pp. 1119-1121.

Résumé
Abstract

On considère ici les feuilletages holomorphes singuliers de codimension 1 dans $C P^{n}, n \geq 6$ , avec une composante de Kupka compacte $K$ . On démontre que $K$ est une intersection complète si $\deg (K)$ n’est pas un carré.

Here we show that a Kupka component $K$ of a codimension 1 singular foliation $F$ of $C P^{n}, n \geq 6$ with $\deg (K)$ not a square is a complete intersection. The result implies the existence of a meromorphic first integral of $F$ .

MR Zbl | 2 citations dans Numdam

DOI : 10.5802/aif.1487

@article{AIF_1995__45_4_1119_0,
     author = {Ballico, Edoardo},
     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}},
     journal = {Annales de l'Institut Fourier},
     pages = {1119--1121},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {45},
     number = {4},
     year = {1995},
     doi = {10.5802/aif.1487},
     mrnumber = {97h:32050},
     zbl = {0831.58046},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1487/}
}

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
SP  - 1119
EP  - 1121
VL  - 45
IS  - 4
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1487/
DO  - 10.5802/aif.1487
LA  - en
ID  - AIF_1995__45_4_1119_0
ER  -

%0 Journal Article
%A Ballico, Edoardo
%T 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
%J Annales de l'Institut Fourier
%D 1995
%P 1119-1121
%V 45
%N 4
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.1487/
%R 10.5802/aif.1487
%G en
%F AIF_1995__45_4_1119_0

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, Tome 45 (1995) no. 4, pp. 1119-1121. doi : 10.5802/aif.1487. http://www.numdam.org/articles/10.5802/aif.1487/

Bibliographie
Cité par

[CS]O. Calvo-Andrade, M. Soares, Chern numbers of a Kupka component, Ann. Inst. Fourier, 44-4 (1994), 1237-1242. | 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. | Zbl

[GML]X. Gomez-Mont, N. Lins, A structural stability of foliations with a meromorphic first integral, Topology, 30 (1990), 315-334. | Zbl

[OSS]Ch. Okonek, M. Schneider, H. Spindler, Vector bundles on complex projective spaces, Progress in Math., 3, Birkhäuser, Basel, 1978. | Zbl

Cité par Sources :