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Manuscripta Mathematica

, Volume 134, Issue 3–4, pp 485–492 | Cite as

Generalization of Peternell, Le Potier and Schneider vanishing theorem

  • F. LaytimiEmail author
Article

Abstract

In this article we give a vanishing result for Dolbeault cohomology groups \({H^{p,q}(X, S^{\nu}E\otimes L)}\), where ν is a positive integer, E is a vector bundle generated by sections and L is an ample line bundle on a smooth projective variety X. We also give a condition for H p,q(X, S ν E) to vanish when E is s-ample and generated by sections. We also give an application related to a result of Barth-Lefschetz type. A general nonvanishing result under the same hypothesis is given to prove the optimality of the vanishing result for some parameter values.

Mathematics Subject Classification (1991)

14F17 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Mathématiques—bât. M2Université Lille 1Villeneuve d’Ascq CedexFrance

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