Hostname: page-component-6898cfcb55-cbk24 Total loading time: 0 Render date: 2026-11-11T09:42:41.034Z Has data issue: false hasContentIssue false
  • English
  • Français

A Vanishing Theorem

Published online by Cambridge University Press:  11 January 2016

F. Laytimi and
W. Nahm
F. Laytimi
Affiliation:
Mathématiques-bât. M2 Université Lille 1 F-59655 Villeneuve d’Ascq Cedex France laytimi@agat.univ-lille1.fr
W. Nahm
Affiliation:
Dublin Institute for Advanced Studies 10 Burlington Road Dublin 4 Ireland wnahm@stp.dias.ie
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

The main result is a general vanishing theorem for the Dolbeault cohomology of an ample vector bundle obtained as a tensor product of exterior powers of some vector bundles. It is also shown that the conditions for the vanishing given by this theorem are optimal for some parameter values.

Keywords

14F17

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 180 , 2005, pp. 35 - 43
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[1] Akizuki, Y. and Nakano, S., Note on Kodaira-Spencer’s proof of Lefschetz theorems, Proc. Jap. Acad., 30 (1954), 266–272.Google Scholar
[2] Bott, R., Homogeneous vector bundles, Ann. Math., 66 (1957), 203–248.CrossRefGoogle Scholar
[3] Demazure, B., A very simple proof of Bott’s theorem, Invent. Math., 33 (1976), 271–220.CrossRefGoogle Scholar
[4] Ein, L. and Lazarsfeld, R., Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension, Invent. Math., 111 (1993), 51–67.CrossRefGoogle Scholar
[5] Fulton, W. and Harris, J., Representation theory, a first course, Graduate texts in Mathematics, Springer Verlag, 1991.Google Scholar
[6] Laytimi, F., On degeneracy loci, International Journal of Mathematics, 6 vol. 7 (1998), 203–220.Google Scholar
[7] Laytimi, F. and Nahm, W., A generalization of Le Potier’s vanishing theorem, Manuscripta math., 113 (2004), 165–189.Google Scholar
[8] Potier, Le, Cohomologie de la Grassmannienne à valeurs dans les puissances extérieures et symetriques du fibré universel, Math. Ann., 226 (1977), 257–270.Google Scholar
[9] Macdonald, I. G., Symmetrics Functions and Hall polynomials, Claredon Press, Oxford, 1976.Google Scholar
[10] Manivel, L., Un théorème d’annulation pour les puissances extérieures d’un fibré ample, J. reine angew. Math., 422 (1991), 91–116.Google Scholar
[11] Manivel, L., théorèmes d’annulation pour les fibrés associés à un fibré ample, Scuola superiore Pisa (1992), 515–565.Google Scholar
[12] Snow, D., Cohomology of twisted holomorphic forms on Grassmann manifolds and quadric hypersurfaces, Math. Ann., 276 (1986), 159–176.CrossRefGoogle Scholar
[13] Sommese, A. J., Submanifold of Abelian Varieties, Math. Ann., 233 (1978), 229–256.Google Scholar