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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^[1] and Kawamata^[2] in 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.

References

^ Viehweg, Eckart (1982), "Vanishing theorems", Journal für die reine und angewandte Mathematik, 335: 1–8, ISSN 0075-4102, MR 0667459
^ 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

Sommese, Andrew J. (2001) [1994], "Kawamata-Viehweg vanishing theorem", Encyclopedia of Mathematics, EMS Press
Kawamata, Yujiro; Matsuda, Katsumi; Matsuki, Kenji (1987). "Introduction to the Minimal Model Problem". Algebraic Geometry, Sendai, 1985. pp. 283–360. doi:10.2969/aspm/01010283. ISBN 978-4-86497-068-6.

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[1] Viehweg, Eckart (1982), "Vanishing theorems", Journal für die reine und angewandte Mathematik, 335: 1–8, ISSN 0075-4102, MR 0667459

[2] 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

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