A vanishing theorem for \(H^ p(\)X, \(Omega^ q(\)B)) on weakly 1-complete manifolds

DOI10.2977/prims/1195185271zbMath0482.32008OpenAlexW1991758040MaRDI QIDQ1162634

Kensho Takegoshi, Takeo Ohsawa

Publication date: 1981

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195185271

zbMATH Keywords

approximation theorem of Runge typeglobal vanishing theoremsemi-positive holomorphic line bundleweakly 1-complete Kaehler manifold

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Holomorphic bundles and generalizations (32L05) Vanishing theorems (32L20) Geometric convexity in several complex variables (32F99)

Related Items

Adjoint type vanishing theorems on pseudoconvex manifolds, Isomorphism theorems for cohomology groups of weakly 1-complete manifolds, (k, s)-POSITIVITY AND VANISHING THEOREMS FOR COMPACT KÄHLER MANIFOLDS, Representation theorems of cohomology on weakly 1-complete manifolds, Cohomology vanishing theorems on weakly 1-complete manifolds, Kodaira vanishing theorems on non-complete algebraic manifolds

Cites Work

• Finiteness theorems on weakly 1-complete manifolds
• A generalization of vanishing theorems for weakly 1-complete manifolds
• On \(H^{p,q}(X,B)\) of weakly 1-complete manifolds
• Weakly 1-complete manifold and Levi problem
• Vanishing theorems for weakly 1-complete manifolds. II
• Simple proofs of Nakano's vanishing theorem and Kazama's approximation theorem for weakly 1-complete manifolds
• Lectures on Levi convexity of complex manifolds and cohomology vanishing theorems. Notes by M.S.Raghunathan
• On the inverse of monoidal transformation
• APPROXIMATION THEOREM AND APPLICATION TO NAKANO'S VANISHING THEOREM FOR WEAKLY 1-COMPLETE MANIFOLDS
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