A Borel-Weil theorem for holomorphic forms

Laurent Manivel; Dennis M. Snow

Compositio Mathematica (1996)

  • Volume: 103, Issue: 3, page 351-365
  • ISSN: 0010-437X

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Manivel, Laurent, and Snow, Dennis M.. "A Borel-Weil theorem for holomorphic forms." Compositio Mathematica 103.3 (1996): 351-365. <http://eudml.org/doc/90475>.

@article{Manivel1996,
author = {Manivel, Laurent, Snow, Dennis M.},
journal = {Compositio Mathematica},
keywords = {Borel-Weil theorem; vanishing properties; Dolbeault cohomology; homogeneous spaces; semisimple complex Lie groups; symmetric space towers; Hermitian symmetric spaces; Nakano vanishing theorem},
language = {eng},
number = {3},
pages = {351-365},
publisher = {Kluwer Academic Publishers},
title = {A Borel-Weil theorem for holomorphic forms},
url = {http://eudml.org/doc/90475},
volume = {103},
year = {1996},
}

TY - JOUR
AU - Manivel, Laurent
AU - Snow, Dennis M.
TI - A Borel-Weil theorem for holomorphic forms
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 103
IS - 3
SP - 351
EP - 365
LA - eng
KW - Borel-Weil theorem; vanishing properties; Dolbeault cohomology; homogeneous spaces; semisimple complex Lie groups; symmetric space towers; Hermitian symmetric spaces; Nakano vanishing theorem
UR - http://eudml.org/doc/90475
ER -

References

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  1. 1 Borel, A.: Linear Algebraic Groups, 2nd ed., Benjamin, New York, 1991. Zbl0186.33201MR1102012
  2. 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. 3 Bott, R.: Homogeneous vector bundles, Ann. Math.66 (1957), 203-248. Zbl0094.35701MR89473
  4. 4 Demailly, J.P.: Vanishing theorems for tensor powers of an ample vector bundle, Invent. Math.91 (1988), 203-220. Zbl0647.14005MR918242
  5. 5 Griffiths, P.: Some geometric and analytic properties of homogeneous complex manifolds, I, Acta Math.110 (1963), 115-155. Zbl0171.44601MR149506
  6. 6 Griffiths, P.: Differential geometry of homogeneous vector bundles, Trans. Amer. Math. Soc.109 (1963), 1-34. Zbl0124.14901MR162248
  7. 7 Humphreys, J.: Introduction to Lie Algebras and Representation Theory, Springer, Berlin, Heidelberg, New York, 1972. Zbl0254.17004MR323842
  8. 8 Kollár, J.: Higher direct images of dualizing sheaves I, Ann. Math.123 (1986), 11-42. Zbl0598.14015MR825838
  9. 9 Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil Theorem, Ann. Math.74 (1961), 329-387. Zbl0134.03501MR142696
  10. 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. Zbl0313.32037MR385179
  11. 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. Zbl0356.32018MR460347
  12. 12 Littlewood, D.E.: The theory of group characters and matrix representations of groups, Oxford Univ. Press, Oxford, 1950. Zbl0038.16504MR2127JFM66.0093.02
  13. 13 Macdonald, I.G.: Symmetric functions and Hall polynomials, Clarendon Press, Oxford, 1979. Zbl0487.20007MR553598
  14. 14 Manivel, L.: Un théorème d'annulation pour les puissances extérieures d' un fibré ample, J. reine angew. Math.422 (1991), 91-116. Zbl0728.14011MR1133319
  15. 15 Manivel, L.: Théorèmes d'annulation pour les fibrés associés à un fibré ample, Scuola Norm. Sup. Pisa19 (1992), 515-565. Zbl0776.32028MR1205883
  16. 16 Snow, D.M.: On the ampleness of homogeneous vector bundles, Trans. Amer. Math. Soc.294 (1986), 585-594. Zbl0588.32038MR825723
  17. 17 Snow, D.M.: Cohomology of twisted holomorphic forms on Grassmann manifolds and quadric hypersurfaces, Math. Ann.276 (1986), 159-176. Zbl0596.32016MR863714
  18. 18 Snow, D.M.: Vanishing theorems on compact hermitian symmetric spaces, Math. Z.198 (1988), 1-20. Zbl0631.32025MR938025
  19. 19 Snow, D.M.: Dolbeault cohomology of homogeneous line bundles, preprint. 
  20. 20 Snow, D.M.: The nef value of homogeneous line bundles and related vanishing theorems, Forum Math.7 (1995), 385-392. Zbl0828.14033MR1325562
  21. 21 Snow, D.M. and Weller, K.: A vanishing theorem for generalized flag manifolds, Arch. Math.64 (1995), 444-451. Zbl0820.32012MR1323922
  22. 22 Tits, J.: Tabellen zu den einfachen Lie Gruppen und ihren Darstellungen, Lecture Notes in Math.40, Springer, Berlin, Heidelberg, New York, 1967. Zbl0166.29703MR218489

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