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arXiv · 1105.1169

Existence of log canonical closures

Christopher D. Hacon·Chenyang Xu
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Abstract

Let $f:X\to U$ be a projective morphism of normal varieties and $(X,Δ)$ a dlt pair. We prove that if there is an open set $U^0\subset U$, such that $(X,Δ)\times_U U^0$ has a good minimal model over $U^0$ and the images of all the non-klt centers intersect $U^0$, then $(X,Δ)$ has a good minimal model over $U$. As consequences we show the existence of log canonical compactifications for open log canonical pairs, and the fact that the moduli functor of stable schemes satisfies the valuative criterion for properness.

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Christopher D. Hacon, Chenyang Xu. 2012-06-28. Existence of log canonical closures. https://arxiv.org/abs/1105.1169

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