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

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.

We will consider codimension one holomorphic foliations represented by sections ω∈H 0 (ℙ 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.

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     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},
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Calvo-Andrade, Omegar; Soares, Marcio G. Chern numbers of a Kupka component. Annales de l'Institut Fourier, Tome 44 (1994) no. 4, pp. 1219-1236. doi : 10.5802/aif.1431. http://archive.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

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