On minimal log discrepancies and kollár components
On minimal log discrepancies and kollár components
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DOI：
10.1017/s0013091521000729
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发表时间：
2018-10
影响因子：
0.7
通讯作者：
Joaqu'in Moraga
中科院分区：
文献类型：
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作者：
Joaqu'in Moraga
本文证明了Fano簇有界性的一个局部蕴涵。更准确地说，我们证明了$d$ -维$a$ -log标准系数的正则奇点，其中承认一个$\n $ -plt爆破，有最小的日志属于一个有限集，只依赖于$d，\，a$和$\n $的差异。这个结果给出了一个自然的几何分层的可能的mld的在一个固定的维度有限集。作为应用，我们证明了例外奇点的最小对数偏差的升链条件。我们还介绍了一个不变的klt奇点有关的总差异的Kollár组件。
In this article, we prove a local implication of boundedness of Fano varieties. More precisely, we prove that $d$ -dimensional $a$ -log canonical singularities with standard coefficients, which admit an $\epsilon$ -plt blow-up, have minimal log discrepancies belonging to a finite set which only depends on $d,\,a$ and $\epsilon$ . This result gives a natural geometric stratification of the possible mld's in a fixed dimension by finite sets. As an application, we prove the ascending chain condition for minimal log discrepancies of exceptional singularities. We also introduce an invariant for klt singularities related to the total discrepancy of Kollár components.