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Vanishing Theorems and Kählerity for Strongly Pseudoconvex Manifolds

Vo Van Tan
Transactions of the American Mathematical Society
Vol. 261, No. 1 (Sep., 1980), pp. 297-302
DOI: 10.2307/1998331
Stable URL: http://www.jstor.org/stable/1998331
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Vanishing Theorems and Kählerity for Strongly Pseudoconvex Manifolds
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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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