Hyperbolicity of singular spaces. (English. French summary) Zbl 1427.32017
Summary: 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.
MSC:
| 32Q45 | Hyperbolic and Kobayashi hyperbolic manifolds |
| 32M15 | Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) |
| 11F41 | Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces |
Keywords:
Green-Griffiths-Lang’s conjectures; bounded symmetric domains; quotient singularities; Hilbert modular varietiesReferences:
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