Positivity on subvarieties and vanishing of higher cohomology
[Positivité sur sous-variétés et annulation de la cohomologie supérieure]
Küronya, Alex1
1 Budapest University of Technology and Economics, Department of Algebra, P.O. Box 91, H-1521 Budapest, Hungary Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Eckerstraße 1, D-79104 Freiburg, Germany
Annales de l'Institut Fourier, Tome 63 (2013) no. 5, pp. 1717-1737.

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.

DOI : 10.5802/aif.2812
Classification : 14C20, 14F17
Keywords: vanishing theorems, generic restrictions of line bundles, q-ampleness.
Mot clés : théorèmes d’annulation, restrictions génériques de fibrés en droites, fibrés q-amples.
Küronya, Alex 1

1 Budapest University of Technology and Economics, Department of Algebra, P.O. Box 91, H-1521 Budapest, Hungary Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Eckerstraße 1, D-79104 Freiburg, Germany 
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Küronya, Alex. Positivity on subvarieties and vanishing of higher cohomology. Annales de l'Institut Fourier, Tome 63 (2013) no. 5, pp. 1717-1737. doi : 10.5802/aif.2812. http://www.numdam.org/articles/10.5802/aif.2812/

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