Log canonical pairs with good augmented base loci

Abstract

Let (X,B) be a projective log canonical pair such that B is a Q-divisor, and that there is a surjective morphism f : X → Z onto a normal variety Z satisfying KX + B ~Q f* M for some big Q-divisor M, and the augmented base locus B+(M) does not contain the image of any log canonical centre of (X, B). We will show that (X,B) has a good log minimal model. An interesting special case is when f is the identity morphism. © The Author(s) 2014.