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Finiteness of fundamental groups

Part of: Local theory Singularities Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  01 February 2017

Zhiyu Tian  and
Chenyang Xu
Zhiyu Tian
Affiliation:
CNRS, Institut Fourier UMR 5582, Université Grenoble Alpes, 38058 Grenoble Cedex 9, France email zhiyu.tian@ujf-grenoble.fr
Chenyang Xu
Affiliation:
Beijing International Center for Mathematical Research, Beijing 100871, China email cyxu@math.pku.edu.cn
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Abstract

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.

Keywords

Kawamata log terminal singularityfundamental groupFano variety

MSC classification

Primary: 14B05: Singularities
Secondary: 14J45: Fano varieties 32S50: Topological aspects
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 2 , February 2017 , pp. 257 - 273
Copyright
© The Authors 2017 

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