Isotriviality of smooth families of varieties of general type

Abstract

In this paper, we proved that a log smooth family of log general type klt pairs with a special (in the sense of Campana) quasi-projective base is isotrivial. As a consequence, we proved the generalized Kebekus–Kovács conjecture Wei and Wu (Hyperbolicity for log smooth families with maximal variation, 2021), Conjecture 1.1, for smooth families of general type varieties as well as log smooth families of log canonical pairs of log general type, assuming the existence of relative good minimal models.