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Polarized pairs, log minimal models, and Zariski decompositions

Published online by Cambridge University Press:  11 January 2016

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

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We continue our study of the relation between log minimal models and various types of Zariski decompositions. Let (X,B) be a projective log canonical pair. We will show that (X,B) has a log minimal model if either KX + B birationally has a Nakayama–Zariski decomposition with nef positive part, or if KX +B is big and birationally has a Fujita–Zariski or Cutkosky–Kawamata–Moriwaki–Zariski decomposition. Along the way we introduce polarized pairs (X,B +P), where (X,B) is a usual projective pair and where P is nef, and we study the birational geometry of such pairs.

Keywords

14E30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 215 , September 2014 , pp. 203 - 224
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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