A note on Lang's conjecture for quotients of bounded domains
Abstract
It was conjectured by Lang that a complex projective manifold is Kobayashi hyperbolic if and only if it is of general type together with all of its subvarieties. We verify this conjecture for projective manifolds whose universal cover carries a bounded, strictly plurisubharmonic function. This includes in particular compact free quotients of bounded domains.
Keywords
Cite
@article{arxiv.1809.02398,
title = {A note on Lang's conjecture for quotients of bounded domains},
author = {Sébastien Boucksom and Simone Diverio},
journal= {arXiv preprint arXiv:1809.02398},
year = {2024}
}
Comments
10 pages, no figures, comments are welcome. v3: following suggestions made by the referee, the exposition has been improved all along the paper, we added a variant of Theorem A which includes manifolds whose universal cover admits a bounded psh function which is strictly psh just at one point, and we added a section of examples. Final version, to appear on \'Epijournal G\'eom. Alg\'ebrique