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We study the hyperbolicity of singular quotients of bounded symmetric domains. We give effective criteria for such quotients to satisfy Green-Griffiths-Langs 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.
We obtain a sharp estimate on the norm of the differential of a harmonic map from the unit disc $mathbb D$ in $mathbb C$ into the unit ball $mathbb B^n$ in $mathbb R^n$, $nge 2$, at any point where the map is conformal. In dimension $n=2$, this gener
In the geometric version of the Langlands correspondence, irregular singular point connections play the role of Galois representations with wild ramification. In this paper, we develop a geometric theory of fundamental strata to study irregular singu
In this paper, we study the behavior of the singular values of Hankel operators on weighted Bergman spaces $A^2_{omega _varphi}$, where $omega _varphi= e^{-varphi}$ and $varphi$ is a subharmonic function. We consider compact Hankel operators $H_{over
Let M be the moduli scheme of canonically polarized manifolds with Hilbert polynomial h. We construct for a given finite set I of natural numbers m>1 with h(m)>0 a projective compactification M of the reduced scheme underlying M such that the ample i
In this note, we introduce the notion of a singular principal G-bundle, associated to a reductive algebraic group G over the complex numbers by means of a faithful representation $varrho^pcolon Glra SL(V)$. This concept is meant to provide an analogo