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.
@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},
volume = {63},
year = {2013},
pages = {1717-1737},
doi = {10.5802/aif.2812},
zbl = {1291.14018},
mrnumber = {3186506},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2013__63_5_1717_0}
}
Küronya, Alex. Positivity on subvarieties and vanishing of higher cohomology. Annales de l'Institut Fourier, Tome 63 (2013) pp. 1717-1737. doi : 10.5802/aif.2812. http://gdmltest.u-ga.fr/item/AIF_2013__63_5_1717_0/
[1] Théorèmes de finitude por la cohomologie des espaces complexes, Bull. Soc. Math. France, Tome 90 (1962), pp. 193-259 | Numdam | MR 150342 | Zbl 0106.05501
[2] The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension (preprint, arXiv:math/0405285) | Zbl 1267.32017
[3] Holomorphic Morse inequalities and asymptotic cohomology groups: a tribute to Bernhard Riemann, Milan Journal of Mathematics, Tome 78 (2010) no. 1, pp. 265-277 | Article | MR 2684780 | Zbl 1205.32017
[4] Holomorphic line bundles with partially vanishing cohomology, Proceedings of the Hirzebruch 65 conference on algebraic geometry (Ramat Gan, 1993), Bar-Ilan University (1996), pp. 165-198 | MR 1360502 | Zbl 0859.14005
[5] Asymptotic invariants of line bundles, Pure Appl. Math. Q., Tome 1 (2005) no. 2, pp. 379-403 (Special Issue: In memory of Armand Borel. Part 1) | Article | MR 2194730 | Zbl 1139.14008
[6] Asymptotic invariants of base loci, Ann. Inst. Fourier (Grenoble), Tome 56 (2006) no. 6, pp. 1701-1734 | Article | Numdam | MR 2282673 | Zbl 1127.14010
[7] Higher cohomology of divisors on projective varieties, Mathematische Annalen, Tome 337 (2007) no. 2, pp. 443-455 | Article | MR 2262793 | Zbl 1127.14012
[8] Vanishing theorems for semipositive line bundles, Algebraic geometry (Tokyo/Kyoto, 1982), Springer, Berlin (Lecture Notes in Math.) Tome 1016 (1983), pp. 519-528 | MR 726440 | Zbl 0522.14010
[9] Algebraic geometry, Springer Verlag, Berlin (1977) | MR 463157 | Zbl 0531.14001
[10] Asymptotic cohomological functions on projective varieties, American Journal of Mathematics, Tome 128 (2006) no. 6, pp. 1475-1519 | Article | MR 2275909 | Zbl 1114.14005
[11] Positivity in Algebraic Geometry I.-II, Springer Verlag, Berlin (Ergebnisse der Mathematik und ihrer Grenzgebiete) Tome 48-49 (2004), pp. 519-528 | MR 2095471 | Zbl 1093.14500
[12] Restricted volumes and divisorial Zariski decompositions (preprint, arXiv:1005.1503) | Zbl 1277.14006
[13] A decomposition of the moving cone of a projective manifold according to the Harder-Narasimhan filtration of the tangent bundle, Albert-Ludwigs-Universität Freiburg (2009) (Ph. D. Thesis) | Zbl 1196.14004
[14] Line bundles with partially vanishing cohomology (preprint, arxiv:1007.3955) | Zbl 1277.14007