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Finiteness of fundamental groups

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.
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https://hal.archives-ouvertes.fr/hal-01975531
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Submitted on : Wednesday, January 9, 2019 - 2:10:57 PM
Last modification on : Tuesday, May 11, 2021 - 11:36:05 AM

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  • HAL Id : hal-01975531, version 1

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Zhiyu Tian, Chenyang Xu. Finiteness of fundamental groups. Compositio Mathematica, Foundation Compositio Mathematica, 2017, 153 (02), pp.257-273. ⟨hal-01975531⟩

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