Existence of log canonical closures

Abstract

Let $f:X\to U$ be a projective morphism of normal varieties and $(X,\Delta )$ a dlt pair. We prove that if there is an open set $U^0\subset U$, such that $(X,\Delta ){\times }_U{U}^0$ has a good minimal model over $U^0$ and the images of all the non-klt centers intersect $U^0$, then $(X,\Delta )$ 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.

References in corpus (5)

• Introduction to the log minimal model program for log canonical pairs
• Moduli of varieties of general type
• Log pluricanonical representations and abundance conjecture
• Quotients by finite equivalence relations
• Existence of log canonical flips and a special LMMP

Cited by in corpus (3)

• Log pluricanonical representations and abundance conjecture
• On Finiteness of B-representation and Semi-log Canonical Abundance
• Demi-Normal Surface Singularities