Families of varieties of general type over compact bases
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 quasiprojective surface. Assuming that the minimal model program holds, this very short paper proves the same result for projective base manifolds Y of arbitrary dimension.
 Publication:

arXiv eprints
 Pub Date:
 April 2007
 arXiv:
 arXiv:0704.2556
 Bibcode:
 2007arXiv0704.2556K
 Keywords:

 Mathematics  Algebraic Geometry;
 14D06;
 14D22