Families of canonically polarized varieties over surfaces

By Stefan Kebekus, S'andor J. Kov'acs. 2005

63 citations recorded by the source corpus.

Shafarevich’s hyperbolicity conjecture asserts that a family of curves over a quasi-projective 1-dimensional base is isotrivial unless the logarithmic Kodaira dimension of the base is positive. More generally it has been conjectured by Viehweg that the base of a smooth family of canonically polarized varieties is of log general type if the family is of maximal variation. In this paper, we relate the variation of a family to the logarithmic Kodaira dimension of the base and give an affirmative answer to Viehweg’s conjecture for families parametrized by surfaces.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a908ecdbc1b124aed03b98d343a6ab6aead13111