Mumford vanishing theorem

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In algebraic geometry, the Mumford vanishing theorem Mumford (1967) states that if L is a semi-ample invertible sheaf with Iitaka dimension at least 2 on a complex projective manifold, then

H^i(X,L^{-1})=0\text{ for }i = 0,1.\

The Mumford vanishing theorem is related to the Ramanujam vanishing theorem, and is generalized by the Kawamata–Viehweg vanishing theorem.