In
algebraic geometry, the Mumford vanishing theorem proved by
Mumford in 1967 states that if ''L'' is a semi-ample
invertible sheaf
In mathematics, an invertible sheaf is a coherent sheaf ''S'' on a ringed space ''X'', for which there is an inverse ''T'' with respect to tensor product of ''O'X''-modules. It is the equivalent in algebraic geometry of the topological notion ...
with
Iitaka dimension at least 2 on a
complex projective manifold, then
:
The Mumford vanishing theorem is related to the
Ramanujam vanishing theorem, and is generalized by the
Kawamata–Viehweg vanishing theorem In algebraic geometry, the Kawamata–Viehweg vanishing theorem is an extension of the Kodaira vanishing theorem, on the vanishing of coherent cohomology groups, to logarithmic pairs, proved independently by Viehweg and Kawamata in 1982.
The th ...
.
References
*
Theorems in algebraic geometry
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