Théorèmes d'annulation pour les fibrés associés à un fibré ample
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 4, pp. 515-565.
@article{ASNSP_1992_4_19_4_515_0,
     author = {Manivel, Laurent},
     title = {Th\'eor\`emes d'annulation pour les fibr\'es associ\'es \`a un fibr\'e ample},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {515--565},
     publisher = {Scuola normale superiore},
     volume = {4e s{\'e}rie, 19},
     number = {4},
     year = {1992},
     mrnumber = {1205883},
     zbl = {0776.32028},
     language = {fr},
     url = {http://www.numdam.org/item/ASNSP_1992_4_19_4_515_0/}
}
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
SP  - 515
EP  - 565
VL  - 19
IS  - 4
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1992_4_19_4_515_0/
LA  - fr
ID  - ASNSP_1992_4_19_4_515_0
ER  - 
%0 Journal Article
%A Manivel, Laurent
%T Théorèmes d'annulation pour les fibrés associés à un fibré ample
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1992
%P 515-565
%V 19
%N 4
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1992_4_19_4_515_0/
%G fr
%F ASNSP_1992_4_19_4_515_0
Manivel, Laurent. Théorèmes d'annulation pour les fibrés associés à un fibré ample. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 4, pp. 515-565. http://www.numdam.org/item/ASNSP_1992_4_19_4_515_0/

[1] R. Bott, Homogeneous vector bundles, Ann. of Math. 66, 203-248 (1957). | MR | Zbl

[2] N. Bourbaki, Eléments de mathématiques, Livre 2, Chapitre 3, Algèbre multilinéaire, Hermann, Paris, 1958.

[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] J.P. Demailly, Vanishing theorems for tensor powers of an ample vector bundle, Invent. Math. 91, 203-220 (1988). | MR | Zbl

[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). | MR | Zbl

[6] J.P. Demailly, Vanishing theorems for tensor powers of a positive vector bundle, Lecture Notes in Math. 1339, Springer Verlag, 1988. | MR | Zbl

[7] B. Demazure, A very simple proof of Bott's theorem, Invent. Math. 33, 271-272 (1976). | MR | Zbl

[8] L. Ein - R. Lazarsfeld, A theorem on the syzygies of smooth projective varieties of arbitrary dimension, preprint.

[9] P.A. Griffiths - J. Harris, Principles of algebraic geometry, Wiley Interscience, New York, 1978. | MR | Zbl

[10] R. Godement, Théorie des faisceaux, Hermann, 1958. | MR | Zbl

[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. | MR | Zbl

[12] M. Kapranov, On the derived category of coherent sheaves on Grassmann manifolds, Math. USSR Izv. 24, 183-192 (1985). | MR | Zbl

[13] D. Knutson, λ -rings and the representation theory of the symmetric group, Lecture Notes 308, Springer, 1973. | MR | Zbl

[14] B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math. 74, 329-387 (1961). | MR | Zbl

[15] B. Kostant, Lie algebra cohomology and generalized Schubert cells, Ann. of Math. 77, 72-144 (1962). | MR | Zbl

[16] H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspekter der Mathematik, Band D1, Braunschweig, Vieweg Sohn, 1985. | MR | Zbl

[17] A. Lascoux, Fonctions de Schur et grassmanniennes, C. R. Acad. Sci. Paris, Sér. A, 281, 851-854 (1975). | MR | Zbl

[18] I.G. Mac Donald, Symmetric functions and Hall polynomials, Oxford, Clarendon Press, 1979. | MR | Zbl

[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). | EuDML | MR | Zbl

[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). | EuDML | MR | Zbl

[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). | MR | Zbl

[22] L. Manivel, Un théorème d'annulation pour les puissances extérieures d'un fibré ample, J. reine angew. Math. 422, 91-116 (1991). | EuDML | MR | Zbl

[23] Th. Peternell - J. Le Potier - M. Schneider, Direct images of sheaves of differentials and the Atiyah class, Math. Z. 196, 75-85 (1987). | EuDML | MR | Zbl

[24] Th. Peternell - J. Le Potier - M. Schneider, Vanishing theorems, linear and quadratic normality, Invent. Math. 87, 573-586 (1987). | EuDML | MR | Zbl

[25] M. Schneider, Ein einfacher Beweis des Verschwindungssatzes für positive holomorphe Vektorraumbündel, Manuscripta Math. 11, 95-101 (1974). | EuDML | MR | Zbl

[26] M. Schneider, Some remarks on vanishing theorems for holomorphic vector bundles, Math. Z. 186, 135-142 (1984). | EuDML | MR | Zbl

[27] B. Shiffman - A.J. Sommese, Vanishing theorems on complex manifolds, Progr. Math. 56, Birkhäuser, 1985. | MR | Zbl

[28] D. Snow, Cohomology of twisted holomorphic forms on Grassmann manifolds and quadric hypersurfaces, Math. Ann. 276, 159-176 (1986). | EuDML | MR | Zbl

[29] D. Snow, On the ampleness of homogeneous vector bundles, Trans. Amer. Math. Soc. 294, 585-594 (1986). | MR | Zbl

[30] A.J. Sommese, Submanifolds of abelian varieties, Math. Ann. 233, 229-256 (1978). | EuDML | MR | Zbl