Mumford vanishing theorem

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.

References

1. 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