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Qfwfq
Qfwfq
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First When is the first chern class of a Kaehler manifold positive/negative?

fixed grammar, and hopefully clarified what sort of sign we are looking for
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Ben McKay
Ben McKay
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I know some examples thatof compact complex manifolds whose first Chern class hasdoes not have a definite sign  (negativeis neither negative, nor positive ornor zero on all complex curves). But I am looking for a necessary and sufficient condition that the first Chern class has a definite sign.

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.

I know some examples of compact complex manifolds whose first Chern class does not have a definite sign  (is neither negative, nor positive nor zero on all complex curves). I am looking for a necessary and sufficient condition that the first Chern class has a definite sign.

added 28 characters in body
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user21574
user21574

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.

I know some examples that first Chern class has not sign. But I am looking for a necessary and sufficient condition that first Chern class has sign.

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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user21574
user21574