TY - JOUR
T1 - Existence of log canonical closures
AU - Hacon, Christopher D.
AU - Xu, Chenyang
N1 - Funding Information:
The first author was partially supported by NSF research grant no. 0757897, the second author was partially supported by NSF research grant no. 0969495. We are grateful to O. Fujino, J. Kollár and J. MKernan for many useful comments and suggestions. We are also in debt to J. Kollár for allowing us to use the materials of [] in Sect. 3. c
PY - 2013/4
Y1 - 2013/4
N2 - 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.
AB - 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.
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U2 - 10.1007/s00222-012-0409-0
DO - 10.1007/s00222-012-0409-0
M3 - Article
AN - SCOPUS:84874988917
SN - 0020-9910
VL - 192
SP - 161
EP - 195
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 1
ER -