On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds
arXiv:math/0101004
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.
arXiv comment36 pages, Latex (4. version): References changed; proof of 5.5 reformulated
References in corpus (5)
- On the isotriviality of families of projective manifolds over curves
- Minimal models and boundedness of stable varieties
- On the Shafarevich conjecture for surfaces of general type over function fields
- A high fibered power of a family of varieties of general type dominates a variety of general type
- Logarithmic Kodaira-Akizuki-Nakano vanishing and Arakelov-Parshin boundedness for singular varieties