Finiteness of fundamental groups

Zhiyu Tian, Chenyang Xu

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 languageEnglish (US)
Pages (from-to)257-273
Number of pages17
JournalCompositio Mathematica
Issue number2
StatePublished - Feb 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • Fano variety
  • Kawamata log terminal singularity
  • fundamental group


Dive into the research topics of 'Finiteness of fundamental groups'. Together they form a unique fingerprint.

Cite this