  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.
