A General Vanishing Theorem


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, S^α E ⊗ (∧^β)E ⊗ L) when S^(α+β)E ⊗ 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

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