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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Vanishing theorems and Kählerity for strongly pseudoconvex manifolds
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by Vo Van Tan
Trans. Amer. Math. Soc. 261 (1980), 297-302
DOI: https://doi.org/10.1090/S0002-9947-1980-0576877-8

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.
References
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Bibliographic Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 261 (1980), 297-302
  • MSC: Primary 32L20; Secondary 32F30, 53C55
  • DOI: https://doi.org/10.1090/S0002-9947-1980-0576877-8
  • MathSciNet review: 576877