# First chern class

I know some examples that first Chern class has not sign(negative, positive or zero). But I am looking for a necessary and sufficient condition that first Chern class has sign.

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What do you mean by "has sign"? Do you mean "is negative"? –  Misha Jun 15 '12 at 23:31
I revised my question –  Hassan Jolany Jun 15 '12 at 23:34
Positive in the sense of Kahler geometry? You can look up Kodaira's embedding theorem. But I'm not sure if that's what you're after. –  Donu Arapura Jun 15 '12 at 23:44
Dear Donu, I mean on Kahler manifolds with complex dimension n –  Hassan Jolany Jun 16 '12 at 0:51