2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60668Consider the moduli functor of canonically polarized complex manifolds with Hilbert polynomial h, and let M_h be the corresponding coarse quasi-projective moduli scheme. We show that M_h is Brody hyperbolic in the following sense: Assume that for some quasi-projective variety U there exists a morphism U --> M_h, quasi-finite over its image, which is induced by a family f: V --> U, belonging to the moduli problem. Then all holomorphic maps from the complex plane to U are constant.36 pages, Latex (4. version): References changed; proof of 5.5 reformulatedAlgebraic GeometryComplex Variables14J10 (Primary) 32Q45, 14D07 (Secondary)text