A fibered power theorem for pairs of log general type

TL;DR

The paper proves a fibered power theorem for families of pairs with log canonical general fibers, showing high fibered powers map to pairs of log general type, with stronger results under additional assumptions.

Contribution

It establishes a new fibered power theorem for pairs of log general type, extending previous results to log canonical and openly canonical fibers.

Findings

High fibered powers map to pairs of log general type after birational modification.

Stronger results hold if the general fiber is openly canonical.

Provides a new approach to understanding the geometry of families of log pairs.

Abstract

Let $f: (X,D) \to B$ be a stably 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.