[Différentielles de jets sur les compactifications toroidales de quotients de la boule]
On donne des estimées explicites pour le volume des différentielles de jets de Green–Griffiths à tout ordre sur une compactification toroïdale d’un quotient de la boule. Pour ce faire, on détermine tout d’abord l’ordre de croissance des différentielles de jets de Green–Griffiths logarithmiques sur ces objets, en utilisant une déformation naturelle de l’espace des jets logarithmiques d’un ordre fixé, vers un fibré projectivisé à poids adéquat. Ensuite, on estime la croissance du nombre de conditions d’annulation au bord qu’une différentielle de jets logarithmique doit satisfaire pour être une différentielle de jets standard.
We give explicit estimates for the volume of the Green–Griffiths jet differentials of any order on a toroidal compactification of a ball quotient. To this end, we first determine the growth of the logarithmic Green–Griffiths jet differentials on these objects, using a natural deformation of the logarithmic jet space of a given order, to a suitable weighted projective bundle. Then, we estimate the growth of the vanishing conditions that a logarithmic jet differential must satisfy over the boundary to be a standard one.
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Keywords: Jet differentials, Ball quotients
Mot clés : Différentielles de jets, quotients de la boule
Cadorel, Benoît 1
CC-BY-ND 4.0
@article{AIF_2020__70_6_2331_0,
author = {Cadorel, Beno{\^\i}t},
title = {Jet differentials on toroidal compactifications of ball quotients},
journal = {Annales de l'Institut Fourier},
pages = {2331--2359},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {70},
number = {6},
year = {2020},
doi = {10.5802/aif.3356},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3356/}
}
TY - JOUR AU - Cadorel, Benoît TI - Jet differentials on toroidal compactifications of ball quotients JO - Annales de l'Institut Fourier PY - 2020 SP - 2331 EP - 2359 VL - 70 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3356/ DO - 10.5802/aif.3356 LA - en ID - AIF_2020__70_6_2331_0 ER -
%0 Journal Article %A Cadorel, Benoît %T Jet differentials on toroidal compactifications of ball quotients %J Annales de l'Institut Fourier %D 2020 %P 2331-2359 %V 70 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3356/ %R 10.5802/aif.3356 %G en %F AIF_2020__70_6_2331_0
Cadorel, Benoît. Jet differentials on toroidal compactifications of ball quotients. Annales de l'Institut Fourier, Tome 70 (2020) no. 6, pp. 2331-2359. doi : 10.5802/aif.3356. https://aif.centre-mersenne.org/articles/10.5802/aif.3356/
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