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.
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.
Keywords: vanishing theorems, generic restrictions of line bundles, q-ampleness.
Mot clés : théorèmes d’annulation, restrictions génériques de fibrés en droites, fibrés q-amples.
@article{AIF_2013__63_5_1717_0, author = { K\"uronya, Alex}, title = {Positivity on subvarieties and vanishing of~higher cohomology}, journal = {Annales de l'Institut Fourier}, pages = {1717--1737}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {63}, number = {5}, year = {2013}, doi = {10.5802/aif.2812}, zbl = {1291.14018}, mrnumber = {3186506}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2812/} }
TY - JOUR AU - Küronya, Alex TI - Positivity on subvarieties and vanishing of higher cohomology JO - Annales de l'Institut Fourier PY - 2013 SP - 1717 EP - 1737 VL - 63 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2812/ DO - 10.5802/aif.2812 LA - en ID - AIF_2013__63_5_1717_0 ER -
%0 Journal Article %A Küronya, Alex %T Positivity on subvarieties and vanishing of higher cohomology %J Annales de l'Institut Fourier %D 2013 %P 1717-1737 %V 63 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2812/ %R 10.5802/aif.2812 %G en %F AIF_2013__63_5_1717_0
Küronya, Alex. Positivity on subvarieties and vanishing of higher cohomology. Annales de l'Institut Fourier, Volume 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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