Vanishing theorems for vector bundles generated by sections

Abstract

In this article we give a vanishing result for the cohomology groups H^p,q(X,Š E⊗ L), where E is a vector bundle generated by sections and L is an ample line bundle on a smooth projective variety X. 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.