- Kodaira embedding theorem
In

mathematics , the**Kodaira embedding theorem**characterisesnon-singular projective varieties , over thecomplex number s, amongst compactKähler manifold s. In effect it says precisely whichcomplex manifold s are defined byhomogeneous polynomial s.Kunihiko Kodaira 's result is that for a compact Kähler manifold "M", withcohomology class in degree 2 defined by theKähler form ω that is an "integral" cohomology class, there is a complex-analytic embedding of "M" intocomplex projective space of some high enough dimension "N". The fact that "M" embeds as analgebraic variety follows by its compactness fromChow's theorem . The Kodaira result gives a sufficient condition; that the integrality is "necessary" is more elementary and was already known.

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