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.
Accepted:
Published online:
DOI: 10.5802/jep.85
Keywords: Green-Griffiths-Lang’s conjectures, bounded symmetric domains, quotient singularities, Hilbert modular varieties
Mot clés : Conjectures de Green-Griffiths-Lang, domaines symétriques bornés, singularités quotients, variétés modulaires de Hilbert
Benoît Cadorel 1; Erwan Rousseau 2; Behrouz Taji 3
CC-BY 4.0
@article{JEP_2019__6__1_0,
author = {Beno{\^\i}t Cadorel and Erwan Rousseau and Behrouz Taji},
title = {Hyperbolicity of singular spaces},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {1--18},
publisher = {\'Ecole polytechnique},
volume = {6},
year = {2019},
doi = {10.5802/jep.85},
mrnumber = {3882579},
zbl = {07003359},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.85/}
}
TY - JOUR AU - Benoît Cadorel AU - Erwan Rousseau AU - Behrouz Taji TI - Hyperbolicity of singular spaces JO - Journal de l’École polytechnique — Mathématiques PY - 2019 SP - 1 EP - 18 VL - 6 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.85/ DO - 10.5802/jep.85 LA - en ID - JEP_2019__6__1_0 ER -
%0 Journal Article %A Benoît Cadorel %A Erwan Rousseau %A Behrouz Taji %T Hyperbolicity of singular spaces %J Journal de l’École polytechnique — Mathématiques %D 2019 %P 1-18 %V 6 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.85/ %R 10.5802/jep.85 %G en %F JEP_2019__6__1_0
Benoît Cadorel; Erwan Rousseau; Behrouz Taji. Hyperbolicity of singular spaces. Journal de l’École polytechnique — Mathématiques, Volume 6 (2019), pp. 1-18. doi : 10.5802/jep.85. https://jep.centre-mersenne.org/articles/10.5802/jep.85/
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