A fibered power theorem for pairs of log general type

Abstract

Let $f:\left(X,D\right)\to B$ be a stable family with log canonical general fiber. We prove that, after a birational modification of the base $\tilde{B}\to B$, there is a morphism from a high fibered power of the family to a pair of log general type. If in addition the general fiber is openly canonical, then there is a morphism from a high fibered power of the original family to a pair openly of log general type.