A note on Lang's conjecture for quotients of bounded domains

Sébastien Boucksom; Simone Diverio

doi:10.46298/epiga.2021.volume5.6050

Sébastien Boucksom ; Simone Diverio - A note on Lang's conjecture for quotients of bounded domains

epiga:6050 - Épijournal de Géométrie Algébrique, March 25, 2021, Volume 5 - https://doi.org/10.46298/epiga.2021.volume5.6050

A note on Lang's conjecture for quotients of bounded domainsArticle

Authors: Sébastien Boucksom ; Simone Diverio

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.

Comment: 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 Géom.
Algébrique

https://doi.org/10.46298/epiga.2021.volume5.6050

Source: arXiv.org:1809.02398

Volume: Volume 5

Published on: March 25, 2021

Accepted on: March 25, 2021

Submitted on: January 24, 2020

Keywords: Mathematics - Complex Variables, Mathematics - Algebraic Geometry, 32Q15 (Primary), 32Q05 (Secondary)

Licence: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)

Funding:

Source : OpenAIRE Graph