Finiteness of fundamental groups

Zhiyu Tian (1) , Chenyang Xu (2)

1 IF - Institut Fourier
2 ASCLEPIOS - Analysis and Simulation of Biomedical Images

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.

Domaines: Mathématiques [math]

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