Polarized pairs, log minimal models, and Zariski decompositions
Polarized pairs, log minimal models, and Zariski decompositions
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DOI：
10.1215/00277630-2781096
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发表时间：
2014-09
影响因子：
0.8
通讯作者：
C. Birkar;Zhengyu Hu
中科院分区：
文献类型：
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作者：
C. Birkar;Zhengyu Hu
摘要我们继续研究对数极小模型与各种类型的Zariski分解之间的关系。设(X，B)是一个射影对数正则对。我们将证明，如果KX+B有Nakayama-Zariski分解且有nef正部，或者KX+B很大且有Fujita-Zariski或Cutkosky-Kawamata-Moriwaki-Zariski分解，则(X，B)有对数极小模型。在此过程中，我们引入了极化对(X，B+P)，其中(X，B)是通常的射影对，其中P是NEF，并且我们研究了这些对的双曲面几何。
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 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.