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

• mathematics - complex variables
• mathematics - algebraic geometry
• 32q15 (primary), 32q05 (secondary)