A Borel-Weil theorem for holomorphic forms
Compositio Mathematica, Tome 103 (1996) no. 3, pp. 351-365.
@article{CM_1996__103_3_351_0,
     author = {Manivel, Laurent and Snow, Dennis M.},
     title = {A {Borel-Weil} theorem for holomorphic forms},
     journal = {Compositio Mathematica},
     pages = {351--365},
     publisher = {Kluwer Academic Publishers},
     volume = {103},
     number = {3},
     year = {1996},
     mrnumber = {1414594},
     zbl = {0859.22004},
     language = {en},
     url = {http://www.numdam.org/item/CM_1996__103_3_351_0/}
}
TY  - JOUR
AU  - Manivel, Laurent
AU  - Snow, Dennis M.
TI  - A Borel-Weil theorem for holomorphic forms
JO  - Compositio Mathematica
PY  - 1996
SP  - 351
EP  - 365
VL  - 103
IS  - 3
PB  - Kluwer Academic Publishers
UR  - http://www.numdam.org/item/CM_1996__103_3_351_0/
LA  - en
ID  - CM_1996__103_3_351_0
ER  - 
%0 Journal Article
%A Manivel, Laurent
%A Snow, Dennis M.
%T A Borel-Weil theorem for holomorphic forms
%J Compositio Mathematica
%D 1996
%P 351-365
%V 103
%N 3
%I Kluwer Academic Publishers
%U http://www.numdam.org/item/CM_1996__103_3_351_0/
%G en
%F CM_1996__103_3_351_0
Manivel, Laurent; Snow, Dennis M. A Borel-Weil theorem for holomorphic forms. Compositio Mathematica, Tome 103 (1996) no. 3, pp. 351-365. http://www.numdam.org/item/CM_1996__103_3_351_0/

1 Borel, A.: Linear Algebraic Groups, 2nd ed., Benjamin, New York, 1991. | MR | Zbl

2 Borel, A.: A spectral sequence for complex analytic bundles, in Hirzebruch, F., Topological Methods in Algebraic Geometry, 3rd ed., Springer, Berlin, Heidelberg, New York, 1978.

3 Bott, R.: Homogeneous vector bundles, Ann. Math. 66 (1957), 203-248. | MR | Zbl

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

5 Griffiths, P.: Some geometric and analytic properties of homogeneous complex manifolds, I, Acta Math. 110 (1963), 115-155. | MR | Zbl

6 Griffiths, P.: Differential geometry of homogeneous vector bundles, Trans. Amer. Math. Soc. 109 (1963), 1-34. | MR | Zbl

7 Humphreys, J.: Introduction to Lie Algebras and Representation Theory, Springer, Berlin, Heidelberg, New York, 1972. | MR | Zbl

8 Kollár, J.: Higher direct images of dualizing sheaves I, Ann. Math. 123 (1986), 11-42. | MR | Zbl

9 Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil Theorem, Ann. Math. 74 (1961), 329-387. | MR | Zbl

10 Le Potier, J.: Annulation de la cohomologie à valeurs dans un fibré vectoriel holomorphe positif de rang quelconque, Math. Ann. 218 (1975), 35-53. | MR | Zbl

11 Le Potier, J.: Cohomologie de la Grassmannienne à valeurs dans les puissances extérieures et symétriques du fibré universel, Math. Ann. 226 (1977), 257-270. | MR | Zbl

12 Littlewood, D.E.: The theory of group characters and matrix representations of groups, Oxford Univ. Press, Oxford, 1950. | JFM | MR

13 Macdonald, I.G.: Symmetric functions and Hall polynomials, Clarendon Press, Oxford, 1979. | MR | Zbl

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

15 Manivel, L.: Théorèmes d'annulation pour les fibrés associés à un fibré ample, Scuola Norm. Sup. Pisa 19 (1992), 515-565. | Numdam | MR | Zbl

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

17 Snow, D.M.: Cohomology of twisted holomorphic forms on Grassmann manifolds and quadric hypersurfaces, Math. Ann. 276 (1986), 159-176. | MR | Zbl

18 Snow, D.M.: Vanishing theorems on compact hermitian symmetric spaces, Math. Z. 198 (1988), 1-20. | MR | Zbl

19 Snow, D.M.: Dolbeault cohomology of homogeneous line bundles, preprint.

20 Snow, D.M.: The nef value of homogeneous line bundles and related vanishing theorems, Forum Math. 7 (1995), 385-392. | MR | Zbl

21 Snow, D.M. and Weller, K.: A vanishing theorem for generalized flag manifolds, Arch. Math. 64 (1995), 444-451. | MR | Zbl

22 Tits, J.: Tabellen zu den einfachen Lie Gruppen und ihren Darstellungen, Lecture Notes in Math. 40, Springer, Berlin, Heidelberg, New York, 1967. | MR | Zbl