Hyperbolicity of singular spaces
Journal de l’École polytechnique - Mathématiques, Volume 6 (2019), pp. 1-18.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.85
Classification: 32Q45,  32M15,  11F41
Keywords: Green-Griffiths-Lang’s conjectures, bounded symmetric domains, quotient singularities, Hilbert modular varieties
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, Volume 6 (2019), pp. 1-18. doi : 10.5802/jep.85. http://www.numdam.org/articles/10.5802/jep.85/

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