A vanishing theorem

Original · EN

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 Hᵖ,q(X,αE⊗ β E⊗ L) when Sα⁺βE ⊗ 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.