Existence of log canonical closures |
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Authors: | Christopher D Hacon Chenyang Xu |
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Institution: | 1. Department of Mathematics, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, UT, 84112, USA 2. Beijing International Center of Mathematics Research, 5 Yiheyuan Road, Haidian District, Beijing, 100871, China
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Abstract: | Let f:X→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?U, such that (X,Δ)× 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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