Küronya, Alex
Positivity on subvarieties and vanishing of higher cohomology  [ Positivité sur sous-variétés et annulation de la cohomologie supérieure ]
Annales de l'institut Fourier, Tome 63 (2013) no. 5 , p. 1717-1737
MR 3186506 | Zbl 1291.14018
doi : 10.5802/aif.2812
URL stable : http://www.numdam.org/item?id=AIF_2013__63_5_1717_0

Classification:  14C20,  14F17
Mots clés: théorèmes d’annulation, restrictions génériques de fibrés en droites, fibrés q-amples.
Nous étudions la relation entre la positivité des restrictions aux intersections complètes générales de fibrés en droites et l’annulation de leur cohomologie supérieure. En application, nous étendons des théorèmes d’annulation classiques de Kawamata-Viehweg et Fujita à des diviseurs potentiellement non-nefs.
We study the relationship between positivity of restriction of line bundles to general complete intersections and vanishing of their higher cohomology. As a result, we extend classical vanishing theorems of Kawamata–Viehweg and Fujita to possibly non-nef divisors.

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