Abstract
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.
Citation
Takeo Ohsawa. "A generalization of Matsushima’s embedding theorem." J. Math. Kyoto Univ. 48 (2) 2008. https://doi.org/10.1215/kjm/1250271418
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