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- Kodaira_embedding_theorem abstract "In mathematics, the Kodaira embedding theorem characterises non-singular projective varieties, over the complex numbers, amongst compact Kähler manifolds. In effect it says precisely which complex manifolds are defined by homogeneous polynomials.Kunihiko Kodaira's result is that for a compact Kähler manifold M, with a Hodge metric, meaning that the cohomology class in degree 2 defined by the Kähler form ω is an integral cohomology class, there is a complex-analytic embedding of M into complex projective space of some high enough dimension N. The fact that M embeds as an algebraic variety follows from its compactness by Chow's theorem. A Kähler manifold with a Hodge metric is occasionally called a Hodge manifold (named after W. V. D. Hodge), so Kodaira's results states that Hodge manifolds are projective. The converse that projective manifolds are Hodge manifolds is more elementary and was already known.".
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- Kodaira_embedding_theorem subject Category:Theorems_in_algebraic_geometry.
- Kodaira_embedding_theorem subject Category:Theorems_in_complex_geometry.
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- Kodaira_embedding_theorem type ComplexManifolds.
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- Kodaira_embedding_theorem comment "In mathematics, the Kodaira embedding theorem characterises non-singular projective varieties, over the complex numbers, amongst compact Kähler manifolds.".
- Kodaira_embedding_theorem label "Kodaira embedding theorem".
- Kodaira_embedding_theorem label "小平埋め込み定理".
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