19 research outputs found

    Generation by Sections and k-Ampleness

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    In the article “Submanifold of abelian varieties”, A.J. Sommese proved that direct sum and tensor product of two vector bundles E and F over a smooth projective variety are k-ample if E and F are k-ample and are generated by global sections. Here we show that the latter condition is not needed

    A General Vanishing Theorem

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    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

    Ximal degeneracy loci and the secant vector bundle

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    A GENERALIZATION OF LE POTIER’S VANISHING THEOREM

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    Consider a vector bundle E of rank d over a compact complex manifold manifold X of dimension n, and a partition R = (r1, r2,...,rm) of weight r = m∑ ri = |R|, where the ri are strictly positive integers wit

    Vanishing theorems for vector bundles generated by sections

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    In this article we give a vanishing result for the cohomology groups Hp,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
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