Families of varieties of general type over compact bases

Details Families of varieties of general type over compact bases Families of varieties of general type over compact bases

2007-04-19

arxiv.org/abs/0704.2556v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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