Finiteness of fundamental groups

被引：10

作者：

Tian, Zhiyu ^{[1
]}

Xu, Chenyang ^{[2
]}

机构：

[1] Univ Grenoble Alpes, Inst Fourier, CNRS, UMR 5582, F-38058 Grenoble 9, France

[2] Beijing Int Ctr Math Res, Beijing 100871, Peoples R China

来源：

COMPOSITIO MATHEMATICA | 2017年 / 153卷 / 02期

关键词：

Kawamata log terminal singularity; fundamental group; Fano variety; COMPLEX; CONNECTEDNESS; BOUNDEDNESS; VARIETIES;

D O I：

10.1112/S0010437X16007867

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：257 / 273

页数：17

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