Hyperbolicity of singular spaces
[Hyperbolicité des espaces singuliers]
Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 1-18.

Nous étudions l’hyperbolicité des quotients singuliers de domaines symétriques bornés. Nous donnons des critères effectifs assurant que de tels quotients vérifient les conjectures de Green-Griffiths-Lang, à la fois dans le cadre analytique et algébrique. Comme application, nous établissons que les variétés modulaires de Hilbert, à part quelques exceptions possibles, satisfont les conjectures attendues.

We study the hyperbolicity of singular quotients of bounded symmetric domains. We give effective criteria for such quotients to satisfy Green-Griffiths-Lang’s conjectures in both analytic and algebraic settings. As an application, we show that Hilbert modular varieties, except for a few possible exceptions, satisfy all expected conjectures.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.85
Classification : 32Q45, 32M15, 11F41
Keywords: Green-Griffiths-Lang’s conjectures, bounded symmetric domains, quotient singularities, Hilbert modular varieties
Mot clés : Conjectures de Green-Griffiths-Lang, domaines symétriques bornés, singularités quotients, variétés modulaires de Hilbert
Cadorel, Benoît 1 ; Rousseau, Erwan 2 ; Taji, Behrouz 3

1 Institut de Mathématiques de Toulouse (IMT), Université Paul Sabatier 118 route de Narbonne, F-31062 Toulouse Cedex 9, France
2 Institut Universitaire de France & Université d’Aix Marseille, CNRS, Centrale Marseille, I2M 39, rue Frédéric Joliot-Curie, 13453 Marseille Cedex 13, France
3 University of Notre Dame, Department of Mathematics 278 Hurley, Notre Dame, IN 46556, USA
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Cadorel, Benoît; Rousseau, Erwan; Taji, Behrouz. Hyperbolicity of singular spaces. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 1-18. doi : 10.5802/jep.85. http://www.numdam.org/articles/10.5802/jep.85/

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