Kodaira embedding theorem
= Kodaira embedding theorem
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The Kodaira embedding theorem says that a compact <complex manifold> carrying a <positive holomorphic line bundle> is projective: sufficiently large <tensor powers> of the bundle have global holomorphic sections defining a <holomorphic embedding> into <Complex projective space>. Conversely, the restriction of $\mathcal O(1)$ gives a positive line bundle on every projective complex manifold.