Open Access
September 2014 Polarized pairs, log minimal models, and Zariski decompositions
Caucher Birkar, Zhengyu Hu
Nagoya Math. J. 215: 203-224 (September 2014). DOI: 10.1215/00277630-2781096


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.


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Caucher Birkar. Zhengyu Hu. "Polarized pairs, log minimal models, and Zariski decompositions." Nagoya Math. J. 215 203 - 224, September 2014.


Published: September 2014
First available in Project Euclid: 16 July 2014

zbMATH: 1314.14028
MathSciNet: MR3263528
Digital Object Identifier: 10.1215/00277630-2781096

Primary: 14E30

Rights: Copyright © 2014 Editorial Board, Nagoya Mathematical Journal

Vol.215 • September 2014
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