Log canonical pairs with good augmented base~loci
type: Item
instance of: scholarly article
zbMATH Open document ID: 1314.14027
DOI: 10.1112/S0010437X13007628
author: Caucher Birkar
author: Zhengyu Hu
published in: Compositio Mathematica
publication date: 2014-08-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/1305.3569
Mathematics Subject Classification ID: 14E30
zbMATH DE Number: 6333822
zbMATH Keywords: minimal models
zbMATH Keywords: log canonical rings
zbMATH Keywords: augmented base loci
MaRDI profile type: Publication
arXiv ID: 1305.3569
cites work: Existence of minimal models for varieties of log general type
cites work: Existence of log canonical flips and a special LMMP
cites work: On existence of log minimal models
cites work: The moduli b-divisor of an lc-trivial fibration
cites work: On the semiampleness of the positive part of CKM Zariski decompositions
cites work: Reduction maps and minimal model theory
cites work: On canonical bundle formulas and subadjunctions
OpenAlex ID: W3100048767
title: Log canonical pairs with good augmented base~loci
review text: The authors show that if \((X,B)\) is a projective log canonical pair, \(B\) is a \(\mathbb Q\)-divisor, \(f:X\to Z\) is a surjective morphism of normal varieties, \(K_X+B\sim _{\mathbb Q}f^*M\) where \(M\) is a big \(\mathbb Q\)-divisor on \(Z\), and the augmented stable base locus \({\mathbf B} _+(M)\) does not contain the image of any log canonical center of \((X,B)\) then \((X,B)\) has a good log minimal model. As a consequence the authors also show that if \((X,B)\) is a projective log canonical pair, \(K_X+B\) is a big \(\mathbb Q\)-divisor and \({\mathbf B} _+(K_X+B)\) does not contain log canonical centers of \((X,B)\), then \((X,B)\) has a good minimal model and hence the log canonical ring \(R(K_X+B)\) is finitely generated.
reviewed by: Christopher Hacon
description: scientific article; zbMATH DE number 6333822