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Finiteness of fundamental groups

Research paper by Zhiyu Tian, Chenyang Xu

Indexed on: 19 Aug '15Published on: 19 Aug '15Published in: Mathematics - Algebraic Geometry



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 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.