# Kähler manifold which is not algebraic

Can someone provide examples of Kähler manifolds which are not algebraic?

This question came to my mind seeing the post of Andrea Ferretti.

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generic complex tori in complex dimension 2 or higher. MR

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You mean those which are not Abelian Varieties? Thanks! –  Anweshi Jan 29 '10 at 20:55
yes that is what I meant.MR –  Mohan Ramachandran Jan 29 '10 at 21:04
ramachndran ==> ramachandran? –  Anweshi Jan 30 '10 at 14:32

You might want to take a look at this previous MO question.

There, I mentioned Voisin's results disproving Kodaira's conjecture (every Kahler manifold is deformation equivalent to a projective manifold).

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