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 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.

16 pages

References in corpus (2)

• The dual complex of Calabi--Yau pairs
• Fundamental groups of symplectic singularities

Cited by in corpus (9)

• K-stability of cubic threefolds
• Fundamental groups of $F$-regular singularities via $F$-signature
• Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds
• The local fundamental group of a Kawamata log terminal singularity is finite
• The Jordan property for local fundamental groups
• Interaction Between Singularity Theory and the Minimal Model Program
• Étale coverings in codimension 1 with applications to Mori Dream Spaces
• On the local étale fundamental group of KLT threefold singularities
• On termination of flips and fundamental groups