Mumford vanishing theorem
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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
- [math]\displaystyle{ H^i(X,L^{-1})=0\text{ for }i = 0,1.\ }[/math]
The Mumford vanishing theorem is related to the Ramanujam vanishing theorem, and is generalized by the Kawamata–Viehweg vanishing theorem.
References
- ↑ Mumford, David (1967), "Pathologies. III", American Journal of Mathematics 89 (1): 94–104, doi:10.2307/2373099, ISSN 0002-9327, http://nrs.harvard.edu/urn-3:HUL.InstRepos:3597248
- Kawamata, Yujiro (1982), "A generalization of Kodaira-Ramanujam's vanishing theorem", Mathematische Annalen 261 (1): 43–46, doi:10.1007/BF01456407, ISSN 0025-5831
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