Jet differentials on toroidal compactifications of ball quotients
Annales de l'Institut Fourier, Volume 70 (2020) no. 6, pp. 2331-2359.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/aif.3356
Classification: 14C20, 32Q05, 32Q45
Keywords: Jet differentials, Ball quotients
Mot clés : Différentielles de jets, quotients de la boule

Cadorel, Benoît 1

1 Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine, Site de Nancy, B.P. 70239, 54506 Vandoeuvre-lès-Nancy Cedex (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Cadorel, Benoît. Jet differentials on toroidal compactifications of ball quotients. Annales de l'Institut Fourier, Volume 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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