Vanishing theorems and Kählerity for strongly pseudoconvex manifolds

Tan, Vo Van

doi:10.1090/S0002-9947-1980-0576877-8

Vanishing theorems and Kählerity for strongly pseudoconvex manifolds
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Trans. Amer. Math. Soc. 261 (1980), 297-302 Request permission

Correction: Trans. Amer. Math. Soc. 291 (1985), 379-380.

Abstract:

A precise vanishing theorem of Kodaira-Nakano type for strongly pseudoconvex manifolds and Nakano semipositive vector bundles is established. This result answers affirmatively a question posed by Grauert and Riemenschneider. However an analogous version of vanishing theorem of Akizuki-Nakano type for strongly pseudoconvex manifolds and Nakano semipositive line bundles does not hold in general. A counterexample for this fact is explicitly constructed. Furthermore we prove that any strongly pseudoconvex manifold with 1-dimensional exceptional subvariety is Kählerian; in particular any strongly pseudoconvex surface is Kählerian.

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