Log canonical pairs with good augmented base loci

TL;DR

This paper proves that certain projective log canonical pairs with specific base locus conditions admit good log minimal models, advancing the understanding of the minimal model program in algebraic geometry.

Contribution

It establishes the existence of good log minimal models for pairs with augmented base loci avoiding log canonical centers, under a particular numerical equivalence condition.

Findings

Existence of good log minimal models under the given conditions.

The result applies even when the morphism is the identity.

Provides new insights into the structure of log canonical pairs.

Abstract

Let $(X,B)$ be a projective log canonical pair such that $B$ is a $\Q$-divisor, and that there is a surjective morphism $f\colon X\to Z$ onto a normal variety $Z$ satisfying: $K_X+B\sim_\Q f^*M$ for some $\Q$-divisor $M$, and the augmented base locus ${\bf{B_+}}(M)$ 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.