Fundamental group of log terminal T-varieties

TL;DR

This paper investigates the fundamental groups of log terminal T-varieties, providing new methods to compute and analyze their topological properties, with applications to Cox rings, Fano varieties, and T-singularities.

Contribution

It introduces a novel approach to study fundamental groups of log terminal T-varieties and applies it to various classes of algebraic varieties and singularities.

Findings

Proves simply connectedness of Cox ring spectra of complex Fano varieties.

Computes fundamental groups of rational log terminal T-varieties of complexity one.

Analyzes local fundamental groups of T-singularities with torus actions.

Abstract

In this article, we introduce an approach to study the fundamental group of a log terminal T-variety. As applications, we prove the simply connectedness of the spectrum of the Cox ring of a complex Fano variety, we compute the fundamental group of a rational log terminal T-varieties of complexity one, and we study the local fundamental group of log terminal T-singularities with a good torus action and trivial GIT decomposition.