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^[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

Sommese, Andrew J. (2001) [1994], "Kawamata–Viehweg vanishing theorem", Encyclopedia of Mathematics, EMS Press

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^ 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

[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

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