Hyperbolicity of singular spaces
Benoit Cadorel (I2M), Erwan Rousseau (IUF, I2M), Behrouz Taji, (DM-Notre Dame)
TL;DR
This paper investigates the hyperbolicity properties of singular quotients of bounded symmetric domains, providing criteria for their alignment with Green-Griffiths-Lang conjectures and applying results to Hilbert modular varieties.
Contribution
It offers effective criteria for hyperbolicity of singular quotients and demonstrates that most Hilbert modular varieties satisfy key conjectures.
Findings
Criteria established for hyperbolicity of singular quotients
Most Hilbert modular varieties satisfy Green-Griffiths-Lang conjectures
Applicable to both analytic and algebraic settings
Abstract
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Meromorphic and Entire Functions · Analytic and geometric function theory