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 $f:X\to Z$ onto a normal variety $Z$ satisfying: $K_X+B\sim_\Q f^*M$ for some $\Q$-divisor $M$, and the augmented base locus ${\mathbf{B}}_{+}(M)$ 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.

17 pages; Final version to appear in Compositio Math

References in corpus (3)

• On existence of log minimal models
• Reduction maps and minimal model theory
• On the semiampleness of the positive part of CKM Zariski decompositions

Cited by in corpus (1)

• Note on quasi-numerically positive log canonical divisors