A vanishing theorem

Abstract

Let $E$ be a vector bundle and $L$ be a line bundle over a smooth projective variety $X$. In this article, we give a condition for the vanishing of Dolbeault cohomology groups of the form $H^{p,q}(X,\SSS^αE\otimes \wedge^β E\otimes L)$ when $S^{\alpha +\beta }E\otimes L$ is ample. This condition is shown to be invariant under the interchange of $p$ and $q$. The optimality of this condition is discussed for some parameter values.

14 pages

References in corpus (1)

• Vanishing theorems for ample vector bundles