Théorèmes d'annulation pour les fibrés associés à un fibré ample

Laurent Manivel

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1992)

  • Volume: 19, Issue: 4, page 515-565
  • ISSN: 0391-173X

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Manivel, Laurent. "Théorèmes d'annulation pour les fibrés associés à un fibré ample." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 19.4 (1992): 515-565. <http://eudml.org/doc/84136>.

@article{Manivel1992,
author = {Manivel, Laurent},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {vanishing theorem; ample vector bundles},
language = {fre},
number = {4},
pages = {515-565},
publisher = {Scuola normale superiore},
title = {Théorèmes d'annulation pour les fibrés associés à un fibré ample},
url = {http://eudml.org/doc/84136},
volume = {19},
year = {1992},
}

TY - JOUR
AU - Manivel, Laurent
TI - Théorèmes d'annulation pour les fibrés associés à un fibré ample
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1992
PB - Scuola normale superiore
VL - 19
IS - 4
SP - 515
EP - 565
LA - fre
KW - vanishing theorem; ample vector bundles
UR - http://eudml.org/doc/84136
ER -

References

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  1. [1] R. Bott, Homogeneous vector bundles, Ann. of Math.66, 203-248 (1957). Zbl0094.35701MR89473
  2. [2] N. Bourbaki, Eléments de mathématiques, Livre 2, Chapitre 3, Algèbre multilinéaire, Hermann, Paris, 1958. Zbl0098.02501
  3. [3] A. Borel, A spectral sequence for complex analytic bundles, in Hirzebruch, F.: Topological methods in algebraic geometry, Berlin-Heidelberg- New York, Springer Verlag, 1966. 
  4. [4] J.P. Demailly, Vanishing theorems for tensor powers of an ample vector bundle, Invent. Math.91, 203-220 (1988). Zbl0647.14005MR918242
  5. [5] J.P. Demailly, Théorèmes d'annulation pour la cohomologie des puissances tensorielles d'un fibré positif, C. R. Acad. Sci. Paris, Sér. I Math., 305, 419-422 (1987). Zbl0627.32022MR916343
  6. [6] J.P. Demailly, Vanishing theorems for tensor powers of a positive vector bundle, Lecture Notes in Math. 1339, Springer Verlag, 1988. Zbl0651.32019MR961475
  7. [7] B. Demazure, A very simple proof of Bott's theorem, Invent. Math.33, 271-272 (1976). Zbl0383.14017MR414569
  8. [8] L. Ein - R. Lazarsfeld, A theorem on the syzygies of smooth projective varieties of arbitrary dimension, preprint. Zbl0814.14040
  9. [9] P.A. Griffiths - J. Harris, Principles of algebraic geometry, Wiley Interscience, New York, 1978. Zbl0408.14001MR507725
  10. [10] R. Godement, Théorie des faisceaux, Hermann, 1958. Zbl0080.16201MR102797
  11. [11] P.A. Griffths, Hermitian differential geometry, Chern classes and positive vector bundles, in Global analysis, papers in honor of K. Kodaira, Princeton Univ. Press, Princeton, 1969, 185-251. Zbl0201.24001MR258070
  12. [12] M. Kapranov, On the derived category of coherent sheaves on Grassmann manifolds, Math. USSR Izv.24, 183-192 (1985). Zbl0564.14023MR733363
  13. [13] D. Knutson, λ -rings and the representation theory of the symmetric group, Lecture Notes308, Springer, 1973. Zbl0272.20008
  14. [14] B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math.74, 329-387 (1961). Zbl0134.03501MR142696
  15. [15] B. Kostant, Lie algebra cohomology and generalized Schubert cells, Ann. of Math.77, 72-144 (1962). Zbl0134.03503MR142697
  16. [16] H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspekter der Mathematik, Band D1, Braunschweig, Vieweg Sohn, 1985. Zbl0669.14003MR768181
  17. [17] A. Lascoux, Fonctions de Schur et grassmanniennes, C. R. Acad. Sci. Paris, Sér. A, 281, 851-854 (1975). Zbl0315.14020MR435094
  18. [18] I.G. Mac Donald, Symmetric functions and Hall polynomials, Oxford, Clarendon Press, 1979. MR553598
  19. [19] J. Le Potier, Annulation de la cohomologie à valeurs dans un fibré vectoriel holomorphe positif de rang quelconque, Math. Ann.218, 35-53 (1975). Zbl0313.32037MR385179
  20. [20] J. Le Potier, Cohomologie de la Grassmannienne à valeurs dans les puissances extérieures et symétriques du fibré universel, Math. Ann.266, 257-270 (1977). Zbl0356.32018MR460347
  21. [21] L. Manivel, Un exemple de non dégénérescence en E2 de la suite spectrale de Borel-Le Potier, C.R. Acad. Sci. Paris Sér. I Math., 311, 31-36 (1990). Zbl0714.14019MR1062924
  22. [22] L. Manivel, Un théorème d'annulation pour les puissances extérieures d'un fibré ample, J. reine angew. Math.422, 91-116 (1991). Zbl0728.14011MR1133319
  23. [23] TH. Peternell - J. Le Potier - M. Schneider, Direct images of sheaves of differentials and the Atiyah class, Math. Z.196, 75-85 (1987). Zbl0662.14006MR907410
  24. [24] TH. Peternell - J. Le Potier - M. Schneider, Vanishing theorems, linear and quadratic normality, Invent. Math.87, 573-586 (1987). Zbl0618.14023MR874037
  25. [25] M. Schneider, Ein einfacher Beweis des Verschwindungssatzes für positive holomorphe Vektorraumbündel, Manuscripta Math.11, 95-101 (1974). Zbl0275.32014MR352551
  26. [26] M. Schneider, Some remarks on vanishing theorems for holomorphic vector bundles, Math. Z.186, 135-142 (1984). Zbl0543.32013MR735057
  27. [27] B. Shiffman - A.J. Sommese, Vanishing theorems on complex manifolds, Progr. Math. 56, Birkhäuser, 1985. Zbl0578.32055MR782484
  28. [28] D. Snow, Cohomology of twisted holomorphic forms on Grassmann manifolds and quadric hypersurfaces, Math. Ann.276, 159-176 (1986). Zbl0596.32016MR863714
  29. [29] D. Snow, On the ampleness of homogeneous vector bundles, Trans. Amer. Math. Soc.294, 585-594 (1986). Zbl0588.32038MR825723
  30. [30] A.J. Sommese, Submanifolds of abelian varieties, Math. Ann.233, 229-256 (1978). Zbl0381.14007MR466647

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