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Two vanishing theorems for holomorphic vector bundles of mixed sign. (English) Zbl 0823.32013

We give (tiny) generalizations of vanishing theorems of Kodaira and Kobayashi for vector bundles over compact complex manifolds. Both yield cohomology vanishing for some vector bundles of mixed sign curvature. Their proofs relies on heat kernel estimates.

MSC:

32L20 Vanishing theorems
32L05 Holomorphic bundles and generalizations
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References:

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