Finiteness of fundamental groups
Finiteness of fundamental groups
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DOI：
10.1112/s0010437x16007867
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发表时间：
2015-08
影响因子：
1.8
通讯作者：
Zhiyu Tian;Chenyang Xu-
中科院分区：
文献类型：
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作者：
Zhiyu Tian;Chenyang Xu-
我们证明了低维对数Fano对的光滑轨迹的基本群的有限性意味着Kawamata对数终端奇点的局部基本群的有限性。作为应用，我们证明了三维KLT奇点的局部基本群和具有正则奇点的三维Fano簇的光滑轨迹的基本群总是有限的。
We show that the finiteness of the fundamental groups of the smooth locus of lower dimensional log Fano pairs would imply the finiteness of the local fundamental group of Kawamata log terminal (klt) singularities. As an application, we verify that the local fundamental group of a three-dimensional klt singularity and the fundamental group of the smooth locus of a three-dimensional Fano variety with canonical singularities are always finite.