Existence of log canonical modifications and its applications
Existence of log canonical modifications and its applications
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DOI：
10.1007/s40879-023-00598-0
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发表时间：
2021-03
影响因子：
0.6
通讯作者：
O. Fujino;K. Hashizume
中科院分区：
文献类型：
--
作者：
O. Fujino;K. Hashizume
本文的主要目的是从极小模型理论的观点出发，建立对奇异性的一些有用的部分解析。首先在适当的假设条件下，建立了正规对的对数正则化的存在性。然后我们全面地恢复了川田在对数正则性上的附加反转。我们还讨论了半正规对的半对数正则化的存在性，并构造了具有几个特别好的性质的dlt爆破。作为一个应用，我们研究了极值有理曲线的长度。
The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some suitable assumptions. Then we recover Kawakita’s inversion of adjunction on log canonicity in full generality. We also discuss the existence of semi-log canonical modifications for demi-normal pairs and construct dlt blow-ups with several extra good properties. As an application, we study lengths of extremal rational curves.