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Sommese Vanishing for non-compact manifolds

D. Kaledin
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Abstract

The Kodaira-Nakano Vanishing Theorem has been generalized to the relative setting by A. Sommese. We prove a version of this theorem for non-compact manifolds. As an apllication, we prove that the cohomology of a fiber of a symplectic contraction is trivial in odd degrees and pure Hodge-Tate in even degrees.

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D. Kaledin. 2005-04-03. Sommese Vanishing for non-compact manifolds. https://arxiv.org/abs/math/0312271

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