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In algebraic geometry, the Mumford vanishing theorem proved by Mumford[1] in 1967 states that if L is a semi-ample invertible sheaf with Iitaka dimension at least 2 on a complex projective manifold, then

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

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

Mumford, David (1967), "Pathologies. III", American Journal of Mathematics, 89 (1): 94–104, doi:10.2307/2373099, ISSN 0002-9327, JSTOR 2373099, MR 0217091

Kawamata, Yujiro (1982), "A generalization of Kodaira-Ramanujam's vanishing theorem", Mathematische Annalen, 261 (1): 43–46, doi:10.1007/BF01456407, ISSN 0025-5831, MR 0675204

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