• Source: Mumford vanishing theorem

In algebraic geometry, the Mumford vanishing theorem proved by Mumford in 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

for

i
=
0
,
1.



{\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



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, S2CID 120101105

Kata Kunci Pencarian:

• Mumford vanishing theorem
• Vanishing theorem
• David Mumford
• Ramanujam vanishing theorem
• Kodaira vanishing theorem
• List of theorems
• Haboush's theorem
• Projective variety
• Borel–Weil–Bott theorem
• George Kempf