论文标题
相对nakayama-zariski分解和广义对的最小模型
Relative Nakayama-Zariski decomposition and minimal models of generalized pairs
论文作者
论文摘要
我们证明了相对nakayama-zariski分解的一些基本特性。我们将它们应用于LC广义对的研究。我们证明了（相对）LC广义对的对数最小模型或Mori纤维空间的存在，由足够的除数偏振。这扩展了Hashizume-hu的结果到广义对。我们还表明，对于任何LC概括性$（x，b+a，{\ bf {m}}）/z $ $（x，b，{\ bf {m}}）/z $具有日志最小模型或mori光纤空间。这是Birkar/Hacon-XU和Hashizume在广义对类别中的结果的类似物，后来证明对完全普遍存在的LC广义翻转至关重要。
We prove some basic properties of the relative Nakayama-Zariski decomposition. We apply them to the study of lc generalized pairs. We prove the existence of log minimal models or Mori fiber spaces for (relative) lc generalized pairs polarized by an ample divisor. This extends a result of Hashizume-Hu to generalized pairs. We also show that, for any lc generalized pair $(X,B+A,{\bf{M}})/Z$ such that $K_X+B+A+{\bf{M}}_X\sim_{\mathbb R,Z}0$ and $B\geq 0,A\geq 0$, $(X,B,{\bf{M}})/Z$ has either a log minimal model or a Mori fiber space. This is an analogue of a result of Birkar/Hacon-Xu and Hashizume in the category of generalized pairs, and is later shown to be crucial to the proof of the existence of lc generalized flips in full generality.
