Chern numbers of a Kupka component

Omegar Calvo-Andrade; Marcio G. Soares

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 4, page 1219-1236
  • ISSN: 0373-0956

Abstract

top
We will consider codimension one holomorphic foliations represented by sections ω H 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.

How to cite

top

Calvo-Andrade, Omegar, and Soares, Marcio G.. "Chern numbers of a Kupka component." Annales de l'institut Fourier 44.4 (1994): 1219-1236. <http://eudml.org/doc/75094>.

@article{Calvo1994,
abstract = {We will consider codimension one holomorphic foliations represented by sections $\omega \in H^0(\{\Bbb P\}^n, \Omega ^1(k))$, 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.},
author = {Calvo-Andrade, Omegar, Soares, Marcio G.},
journal = {Annales de l'institut Fourier},
keywords = {Chern class; residues; Kupka set; holomorphic foliations; complete intersection},
language = {eng},
number = {4},
pages = {1219-1236},
publisher = {Association des Annales de l'Institut Fourier},
title = {Chern numbers of a Kupka component},
url = {http://eudml.org/doc/75094},
volume = {44},
year = {1994},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 4
SP - 1219
EP - 1236
AB - We will consider codimension one holomorphic foliations represented by sections $\omega \in H^0({\Bbb P}^n, \Omega ^1(k))$, 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.
LA - eng
KW - Chern class; residues; Kupka set; holomorphic foliations; complete intersection
UR - http://eudml.org/doc/75094
ER -

References

top
  1. [B] W. BARTH, Some properties of stable rank-2 vector bundles on Pn, Math. Ann., 226 (1977), 125-150. Zbl0332.32021MR55 #2905
  2. [BB] P. BAUM, R. BOTT, Singularities of holomorphic foliations, Journal on Differential Geometry, 7 (1972), 279-342. Zbl0268.57011MR51 #14092
  3. [BCh] E. BALLICO, L. CHIANTINI, On smooth subcanonical varieties of codimension 2 in Pn n ≥ 4, Annali di Matematica, (1983), 99-117. Zbl0549.14015MR86d:14047
  4. [CL] D. CERVEAU, A. LINS, Codimension one holomorphic foliations with Kupka components. Zbl0823.32014
  5. [GS] H. GRAUERT, M. SCHNEIDER, Komplexe Unterräume und holomorphe Vektorraumbündel von Rang zwei, Math. Ann., 230 (1977), 75-90. Zbl0412.32014MR58 #1279
  6. [GH] Ph. GRIFFITHS, J. HARRIS, Principles of Algebraic Geometry, Pure & Applied Math., Wiley Intersc., New York, 1978. Zbl0408.14001
  7. [G] R. GODEMENT, Topologie algébrique et théorie de faisceaux, Actualités Scientifiques et Industrielles, Herman, Paris, 1952. 
  8. [GML] X. GÓMEZ-MONT, N. LINS, A structural stability of foliations with a meromorphic first integral, Topology, 30 (1990), 315-334. Zbl0735.57014
  9. [H] R. HARTSHORNE, Varieties of small codimension in projective space, Bull. of the AMS, 80 (1974), 1017-1032. Zbl0304.14005MR52 #5688
  10. [H1] R. HARTSHORNE, Stable vector bundles of rank 2 on P3, Math. Ann., 238 (1978), 229-280. Zbl0411.14002MR80c:14011
  11. [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. Zbl0581.14035MR86m:14036
  12. [M] A. MEDEIROS, Structural stability of integrable differential forms, Geometry and Topology, LNM, Springer, New York, 1977, pp. 395-428. Zbl0363.58007MR56 #9561
  13. [OSS] Ch. OKONEK, M. SCHNEIDER, H. SPINDLER, Vector Bundles on Complex Projective spaces, Progress in Math., 3, Birkhauser, Basel, 1978. 
  14. [R] Z. RAN, On projective varieties of codimension 2, Invent. Math., 73 (1983), 333-336. Zbl0521.14018MR85g:14063

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.