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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 (1982) and Kawamata (1982).

The theorem states that if L is a big nef line bundle (for example, an ample line bundle) on a complex projective manifold with canonical line bundle K, then the coherent cohomology groups Hi(L⊗K) vanish for all positive i.


Sommese, Andrew J. (2001), "K/k120060", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104
Viehweg, Eckart (1982), "Vanishing theorems", Journal für die reine und angewandte Mathematik 335: 1–8, ISSN 0075-4102, MR667459
Kawamata, Yujiro (1982), "A generalization of Kodaira-Ramanujam's vanishing theorem", Mathematische Annalen 261 (1): 43–46, doi:10.1007/BF01456407, ISSN 0025-5831, MR675204

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