Finiteness of algebraic fundamental groups

TL;DR

This paper proves that the algebraic local fundamental group of klt singularities and the algebraic fundamental group of the smooth locus of log Fano varieties are finite, advancing understanding in algebraic geometry.

Contribution

It establishes the finiteness of algebraic fundamental groups for certain classes of singularities and varieties, a significant theoretical advancement.

Findings

Algebraic local fundamental groups of klt singularities are finite.

Algebraic fundamental groups of smooth loci of log Fano varieties are finite.

Provides new insights into the structure of algebraic fundamental groups.

Abstract

We show that the algebraic local fundamental group of any klt singularity as well as the algebraic fundamental group of the smooth locus of any log Fano variety are finite.