Hyperbolicity of singular spaces

Benoit Cadorel (1) , Erwan Rousseau (2, 1) , Behrouz Taji (3)

1 I2M - Institut de Mathématiques de Marseille
2 IUF - Institut universitaire de France
3 DM-Notre Dame - Department of Mathematics

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.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Benoit Cadorel, Erwan Rousseau, Behrouz Taji. Hyperbolicity of singular spaces. Journal de l'École polytechnique — Mathématiques, 2019. ⟨hal-01622037v2⟩