[Isotrivialité et caractère spécial pour les feuilletages algébriques réguliers]
Nous montrons l’isotrivialité des feuilles d’un feuilletage partout régulier et à feuilles compactes sur une variété quasi-projective lorsque la base orbifolde de la famille des feuilles est spéciale. Cette dernière condition signifie que, pour tout , la puissance extérieure -ième de l’extension logarithmique du fibré conormal de ne contient aucun sous-faisceau de rang un de dimension de Kodaira maximale . Cette condition est satisfaite, par exemple, dans le cas très particulier où la dimension de Kodaira du déterrminant de l’extension logarithmique du fibré conormal est nulle. Des exemples de cette situation sont fournis par les sous-variétés « algébriquement coisotropes » des variétés hyperkählériennes irréductibles projectives.
We show that an everywhere regular foliation on a quasi-projective manifold, such that all of its leaves are compact with semi-ample canonical bundle, has isotrivial family of leaves when the orbifold base of this family is special. The specialness condition means that for any , the -th exterior power of the logarithmic extension of its conormal bundle does not contain any rank-one subsheaf of maximal possible Kodaira dimension . This condition is satisfied, for example, in the very particular case when the Kodaira dimension of the determinant of the logarithmic extension of the conormal bundle vanishes. Motivating examples are given by the “algebraically coisotropic” submanifolds of irreducible hyperkähler projective manifolds.
Keywords: algebraic foliations, isotriviality, orbifold divisors, special quasi-projective manifolds
Mots-clés : feuilletage algébrique, isotrivialité, diviseurs orbifoldes, varétés quasi-projectives spéciales
Amerik, Ekaterina 1, 2 ; Campana, Frédéric 3, 4
CC-BY-ND 4.0
@article{AIF_2018__68_7_2923_0,
author = {Amerik, Ekaterina and Campana, Fr\'ed\'eric},
title = {Specialness and {Isotriviality} for {Regular} {Algebraic} {Foliations}},
journal = {Annales de l'Institut Fourier},
pages = {2923--2950},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {68},
number = {7},
year = {2018},
doi = {10.5802/aif.3231},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3231/}
}
TY - JOUR AU - Amerik, Ekaterina AU - Campana, Frédéric TI - Specialness and Isotriviality for Regular Algebraic Foliations JO - Annales de l'Institut Fourier PY - 2018 SP - 2923 EP - 2950 VL - 68 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3231/ DO - 10.5802/aif.3231 LA - en ID - AIF_2018__68_7_2923_0 ER -
%0 Journal Article %A Amerik, Ekaterina %A Campana, Frédéric %T Specialness and Isotriviality for Regular Algebraic Foliations %J Annales de l'Institut Fourier %D 2018 %P 2923-2950 %V 68 %N 7 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3231/ %R 10.5802/aif.3231 %G en %F AIF_2018__68_7_2923_0
Amerik, Ekaterina; Campana, Frédéric. Specialness and Isotriviality for Regular Algebraic Foliations. Annales de l'Institut Fourier, Tome 68 (2018) no. 7, pp. 2923-2950. doi : 10.5802/aif.3231. https://aif.centre-mersenne.org/articles/10.5802/aif.3231/
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