Journal of Mathematics of Kyoto University

A generalization of Matsushima’s embedding theorem

Ohsawa, Takeo

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Let $M$ be a compact complex manifold and let $L \rightarrow M$ be a homorphic line bundle whose curvature form is everywhere of signature $(s_+, s_-)$. Under some conditions on the curvature form of $L$, it is show that $K \otimes L^{\otimes m}$ admits, for some $K$ and sufficiently large $m \in \mathbb{N}$, $C^{\infty}$ sections $t_0, \ldots, t_N$ such that the ratio $(t_0 : \cdots : t_N)$ embeds $M$ holomorphically in $s_+$ variables and antiholomorphically in $s_-$ variables. The result extends the Kodaira's embedding theorem as well as aresult of Matsushima for complex tori.

Article information

J. Math. Kyoto Univ., Volume 48, Number 2 (2008).

First available in Project Euclid: 14 August 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32E40: The Levi problem 32V40: Real submanifolds in complex manifolds
Secondary: 53C40


Ohsawa, Takeo. A generalization of Matsushima’s embedding theorem. J. Math. Kyoto Univ. 48 (2008), no. 2, . doi:10.1215/kjm/1250271418.

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