Chern numbers of a Kupka component
Annales de l'Institut Fourier, Volume 44 (1994) no. 4, pp. 1219-1236.

We will consider codimension one holomorphic foliations represented by sections ωH 0 ( n ,Ω 1 (k)), and having a compact Kupka component K. We show that the Chern classes of the tangent bundle of K behave like Chern classes of a complete intersection 0 and, as a corollary we prove that K is a complete intersection in some cases.

On considère les feuilletages holomorphes singuliers de codimension 1 dans le projectif complexe de dimension n qui admettent une composante de Kupka compacte K. On montre que les classes de Chern du fibré tangent à K se comportent comme les classes de Chern d’une intersection complète et, comme corollaire, on déduit que K est une intersection complète dans certains cas.

@article{AIF_1994__44_4_1219_0,
     author = {Calvo-Andrade, Omegar and Soares, Marcio G.},
     title = {Chern numbers of a {Kupka} component},
     journal = {Annales de l'Institut Fourier},
     pages = {1219--1236},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {44},
     number = {4},
     year = {1994},
     doi = {10.5802/aif.1431},
     zbl = {0811.32024},
     mrnumber = {95m:32045},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1431/}
}
TY  - JOUR
AU  - Calvo-Andrade, Omegar
AU  - Soares, Marcio G.
TI  - Chern numbers of a Kupka component
JO  - Annales de l'Institut Fourier
PY  - 1994
DA  - 1994///
SP  - 1219
EP  - 1236
VL  - 44
IS  - 4
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1431/
UR  - https://zbmath.org/?q=an%3A0811.32024
UR  - https://www.ams.org/mathscinet-getitem?mr=95m:32045
UR  - https://doi.org/10.5802/aif.1431
DO  - 10.5802/aif.1431
LA  - en
ID  - AIF_1994__44_4_1219_0
ER  - 
%0 Journal Article
%A Calvo-Andrade, Omegar
%A Soares, Marcio G.
%T Chern numbers of a Kupka component
%J Annales de l'Institut Fourier
%D 1994
%P 1219-1236
%V 44
%N 4
%I Association des Annales de l’institut Fourier
%U https://doi.org/10.5802/aif.1431
%R 10.5802/aif.1431
%G en
%F AIF_1994__44_4_1219_0
Calvo-Andrade, Omegar; Soares, Marcio G. Chern numbers of a Kupka component. Annales de l'Institut Fourier, Volume 44 (1994) no. 4, pp. 1219-1236. doi : 10.5802/aif.1431. http://www.numdam.org/articles/10.5802/aif.1431/

[B] W. Barth, Some properties of stable rank-2 vector bundles on Pn, Math. Ann., 226 (1977), 125-150. | MR | Zbl

[BB] P. Baum, R. Bott, Singularities of holomorphic foliations, Journal on Differential Geometry, 7 (1972), 279-342. | MR | Zbl

[BCh] E. Ballico, L. Chiantini, On smooth subcanonical varieties of codimension 2 in Pn n ≥ 4, Annali di Matematica, (1983), 99-117. | MR | Zbl

[CL] D. Cerveau, A. Lins, Codimension one holomorphic foliations with Kupka components.

[GS] H. Grauert, M. Schneider, Komplexe Unterräume und holomorphe Vektorraumbündel von Rang zwei, Math. Ann., 230 (1977), 75-90. | MR | Zbl

[GH] Ph. Griffiths, J. Harris, Principles of Algebraic Geometry, Pure & Applied Math., Wiley Intersc., New York, 1978. | Zbl

[G] R. Godement, Topologie algébrique et théorie de faisceaux, Actualités Scientifiques et Industrielles, Herman, Paris, 1952.

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

[H] R. Hartshorne, Varieties of small codimension in projective space, Bull. of the AMS, 80 (1974), 1017-1032. | MR | Zbl

[H1] R. Hartshorne, Stable vector bundles of rank 2 on P3, Math. Ann., 238 (1978), 229-280. | MR | Zbl

[HS] A. Holme, M. Schneider, A computer aided approach to codimension 2 subvarieties of Pn, n ≥ 6, J. Reine Angew. Math., 357 (1985), 205-220. | MR | Zbl

[M] A. Medeiros, Structural stability of integrable differential forms, Geometry and Topology, LNM, Springer, New York, 1977, pp. 395-428. | MR | Zbl

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

[R] Z. Ran, On projective varieties of codimension 2, Invent. Math., 73 (1983), 333-336. | MR | Zbl

Cited by Sources: