Kawamata–Viehweg vanishing theorem
From HandWiki
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, http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN243919689_0335&DMDID=dmdlog4
- ↑ Kawamata, Yujiro (1982), "A generalization of Kodaira-Ramanujam's vanishing theorem", Mathematische Annalen 261 (1): 43–46, doi:10.1007/BF01456407, ISSN 0025-5831
- Hazewinkel, Michiel, ed. (2001), "Kawamata-Viehweg vanishing theorem", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Main_Page
- 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. https://projecteuclid.org/euclid.aspm/1525310275.
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