On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds

Details On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds

2000-12-31

arxiv.org/abs/math/0101004v4

Mathematics

Algebraic Geometry

36 pages, Latex (4. version): References changed; proof of 5.5 reformulated

Scientific paper

Consider 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.

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