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Log canonical pairs with good augmented base loci

Part of: Birational geometry

Published online by Cambridge University Press:  26 March 2014

Caucher Birkar  and
Zhengyu Hu
Caucher Birkar
Affiliation:
DPMMS, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge, CB3 0WB, UK email c.birkar@dpmms.cam.ac.uk
Zhengyu Hu
Affiliation:
DPMMS, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge, CB3 0WB, UK email zh262@dpmms.cam.ac.uk
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Abstract

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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.

Keywords

minimal modelslog canonical ringsaugmented base loci

MSC classification

Secondary: 14E30: Minimal model program (Mori theory, extremal rays)
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 4 , April 2014 , pp. 579 - 592
Copyright
© The Author(s) 2014 

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