English

On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds

Algebraic Geometry 2007-05-23 v4 Complex Variables

Abstract

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.

Keywords

Cite

@article{arxiv.math/0101004,
  title  = {On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds},
  author = {Eckart Viehweg and Kang Zuo},
  journal= {arXiv preprint arXiv:math/0101004},
  year   = {2007}
}

Comments

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