Existence of log canonical closures
Hacon, Christopher D. ; Xu, Chenyang
arXiv, 1105.1169 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2011-05-05
Classification:  Mathematics - Algebraic Geometry 
@article{1105.1169,
     author = {Hacon, Christopher D. and Xu, Chenyang},
     title = {Existence of log canonical closures},
     journal = {arXiv},
     volume = {2011},
     number = {0},
     year = {2011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1105.1169}
}

Hacon, Christopher D.; Xu, Chenyang. Existence of log canonical closures. arXiv, Tome 2011 (2011) no. 0, . http://gdmltest.u-ga.fr/item/1105.1169/