FAMILIES OVER A BASE WITH A BIRATIONALLY NEF TANGENT BUNDLE

It is a well-known consequence of the Torelli theorem that a smooth pr ojective family of curves of genus at least 2 over a projective ration al or elliptic curve is isotrivial, that is, the fibres of the family are isomorphic. Since the automorphism group of a curve of genus at le ast 2 is finite, this also implies that the family becomes trivial aft er a finite base change. The above statement was generalized for smoot h projective families of minimal surfaces of general type in [Migliori ni95], and for smooth projective families of varieties (of arbitrary d imension) with ample canonical bundle in [Kovics96]. Both articles stu died families over curves. The aim of this article is to present a fur ther generalization, namely let the base of the family have arbitrary dimension.