Existence of log canonical closures

Christopher D. Hacon, Chenyang Xu

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


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 U0⊂U, such that (X,Δ)×UU0 has a good minimal model over U0 and the images of all the non-klt centers intersect U0, 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.

Original languageEnglish (US)
Pages (from-to)161-195
Number of pages35
JournalInventiones Mathematicae
Issue number1
StatePublished - Apr 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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