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- Q6425088 subject Q8851964.
- Q6425088 subject Q8851967.
- Q6425088 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.".
- Q6425088 wikiPageExternalLink lecture-notes.
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- Q6425088 wikiPageWikiLink Q8851964.
- Q6425088 wikiPageWikiLink Q8851967.
- Q6425088 comment "In mathematics, the Kodaira embedding theorem characterises non-singular projective varieties, over the complex numbers, amongst compact Kähler manifolds.".
- Q6425088 label "Kodaira embedding theorem".