Some Properties
The existence of an ample line bundle on X is equivalent to X being a projective variety, so this is the case for Fano varieties. The Kodaira vanishing theorem implies that the higher cohomology groups of the structure sheaf vanish for . In particular, the first Chern class induces an isomorphism
A Fano variety is simply connected and is uniruled, in particular it has Kodaira dimension −∞.
Read more about this topic: Fano Variety
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