Vanishing theorems for ample vector bundles

Mathematics – Algebraic Geometry

Scientific paper

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12 pages, LaTeX2e

Scientific paper

10.1007/s002220050126

We prove a general vanishing theorem for the cohomology of products of symmetric and skew-symmetric powers of an ample vector bundle on a smooth complex projective variety. Special cases include an extension of classical theorems of Griffiths and Le Potier to the whole Dolbeault cohomology, and an answer to a problem raised by Demailly. An application to degeneracy loci is given.

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