Families of varieties of general type over compact bases
Algebraic Geometry
2007-05-23 v1
Abstract
Let f: X -> Y be a smooth family of canonically polarized complex varieties over a smooth base. Generalizing the classical Shafarevich hyperbolicity conjecture, Viehweg conjectured that Y is necessarily of log general type if the family has maximal variation. A somewhat stronger and more precise version of Viehweg's conjecture was shown by the authors in arXiv:math/0511378 in the case where Y is a quasi-projective surface. Assuming that the minimal model program holds, this very short paper proves the same result for projective base manifolds Y of arbitrary dimension.
Keywords
Cite
@article{arxiv.0704.2556,
title = {Families of varieties of general type over compact bases},
author = {Stefan Kebekus and Sandor Kovacs},
journal= {arXiv preprint arXiv:0704.2556},
year = {2007}
}