[Diviseurs de base de fibrés en droites gros et nefs sur des variétés symplectiques irréductibles]
Nous décrivons quels fibrés en droites gros et nefs, sur des variétés symplectiques irréductibles, ont des diviseurs de base, sous certaines conditions relatives au type de déformation dont nous nous attendons à ce qu’elles soient vraies pour toutes les variétés symplectiques irréductibles. En particulier, nous montrons que de tels diviseurs de base sont toujours réduits et irréductibles. Nous appliquons ces résultats pour comprendre le comportement après déformation des diviseurs de base des fibrés en droites gros et nefs. Nous terminons en donnant une déscription très explicite pour les variétés de types et .
Under some conditions on the deformation type, which we expect to be satisfied for arbitrary irreducible symplectic varieties, we describe which big and nef line bundles on irreducible symplectic varieties have base divisors. In particular, we show that such base divisors are always irreducible and reduced. This is applied to understand the behaviour of divisorial base components of big and nef line bundles under deformations and for -type and -type.
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Keywords: Irreducible symplectic varieties, hyperkähler manifolds, base divisors, Fujita’s conjecture
Mot clés : Variétés symplectiques irréductibles, variétés hyperkähleriennes, diviseurs de base, conjecture de Fujita
CC-BY-ND 4.0
@article{AIF_2023__73_2_609_0,
author = {Rie{\ss}, Ulrike},
title = {Base divisors of big and nef line bundles on irreducible symplectic varieties},
journal = {Annales de l'Institut Fourier},
pages = {609--633},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {73},
number = {2},
year = {2023},
doi = {10.5802/aif.3530},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3530/}
}
TY - JOUR AU - Rieß, Ulrike TI - Base divisors of big and nef line bundles on irreducible symplectic varieties JO - Annales de l'Institut Fourier PY - 2023 SP - 609 EP - 633 VL - 73 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3530/ DO - 10.5802/aif.3530 LA - en ID - AIF_2023__73_2_609_0 ER -
%0 Journal Article %A Rieß, Ulrike %T Base divisors of big and nef line bundles on irreducible symplectic varieties %J Annales de l'Institut Fourier %D 2023 %P 609-633 %V 73 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3530/ %R 10.5802/aif.3530 %G en %F AIF_2023__73_2_609_0
Rieß, Ulrike. Base divisors of big and nef line bundles on irreducible symplectic varieties. Annales de l'Institut Fourier, Tome 73 (2023) no. 2, pp. 609-633. doi : 10.5802/aif.3530. https://aif.centre-mersenne.org/articles/10.5802/aif.3530/
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