= Solution
A <holomorphic line bundle> is <ample> when some positive <tensor power> is <very ample>, so its sections define an embedding into <Complex projective space>. It is a <positive holomorphic line bundle> when it has a <Hermitian metric> with positive Chern curvature $iF_\nabla$. The <Kodaira embedding theorem> says that a compact <complex manifold> carrying a positive holomorphic line bundle is projective; sufficiently high tensor powers give a <holomorphic embedding> into projective space.
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