Talk:Kodaira vanishing theorem

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--Cronholm¹⁴⁴ 03:33, 16 June 2007 (UTC)

Also called the Kodaira-Nakano Vanishing Theorem:

$H q (M,Ω p (L)) = 0$ for p+q > n

A holomorphic line bundle is positive if it admits a hermitian metric such that the associated connection has curvature tensor $Θ$ satisfying:

$-i<\Theta(x);v,v^*> \in Hom(L_x,L_x)=\mathbb{C}$ is positive for all v in the holomorphic tangent bundle of M at x.