Finiteness of fundamental groups

Zhiyu Tian; Chenyang Xu

doi:10.1112/S0010437X16007867

Finiteness of fundamental groups

Zhiyu Tian, Chenyang Xu

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English (US)
Pages (from-to)	257-273
Number of pages	17
Journal	Compositio Mathematica
Volume	153
Issue number	2
DOIs	https://doi.org/10.1112/S0010437X16007867
State	Published - Feb 1 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Fano variety
Kawamata log terminal singularity
fundamental group

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10.1112/S0010437X16007867

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AB - 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.

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KW - Kawamata log terminal singularity

KW - fundamental group

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Finiteness of fundamental groups

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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