Vol. 10, No. 7, 2016

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A fibered power theorem for pairs of log general type

Kenneth Ascher and Amos Turchet

Vol. 10 (2016), No. 7, 1581–1600
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 $\stackrel{˜}{B}\to B$, 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.

Keywords
log general type, moduli of stable pairs, Lang–Vojta
Mathematical Subject Classification 2010
Primary: 14J10
Secondary: 14J29, 14E99, 14G05