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Log canonical pairs with good augmented base loci
- Part of
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- Journal:
- Compositio Mathematica / Volume 150 / Issue 4 / April 2014
- Published online by Cambridge University Press:
- 26 March 2014, pp. 579-592
- Print publication:
- April 2014
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- Article
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Let
$(X,B)$ be a projective log canonical pair such that 
$B$ is a 
$\mathbb{Q}$-divisor, and that there is a surjective morphism 
$f: X\to Z$ onto a normal variety 
$Z$ satisfying 
$K_X+B\sim _{\mathbb{Q}} f^*M$ for some big 
$\mathbb{Q}$-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.
