On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds
Abstract
Consider the moduli functor of canonically polarized complex manifolds with Hilbert polynomial h, and let Mh be the corresponding coarse quasi-projective moduli scheme. We show that Mh is Brody hyperbolic in the following sense: Assume that for some quasi-projective variety U there exists a morphism U --> Mh, 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.
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