On log minimal models and Zariski decompositions II

2013/02/16 by Caucher Birkar, Birkar, Caucher, Zhengyu Hu +1 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.1302.4015

17 pages

arxiv created 2013/02/16 · arxiv updated 2013/02/19

Abstract

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 K_X+B birationally has a Nakayama-Zariski decomposition with nef positive part, or that K_X+B is big and birationally it has a Fujita or CKM Zariski decomposition. Along the way we introduce polarized pairs (X,B+P) where (X,B) is a usual projective pair and P is nef, and study the birational geometry of such pairs.

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