Infinite transitivity on universal torsors

TL;DR

This paper proves that the automorphism group of the universal torsor over certain algebraic varieties acts infinitely transitively, expanding understanding of symmetries in algebraic geometry.

Contribution

It establishes infinite transitivity of automorphism groups on universal torsors over a broad class of algebraic varieties.

Findings

Automorphism group acts infinitely transitively on universal torsors.

Identifies classes of varieties with such universal torsor coverings.

Enhances understanding of symmetry properties in algebraic geometry.

Abstract

Let X be an algebraic variety covered by open charts isomorphic to the affine space and q: X' \to X be the universal torsor over X. We prove that the automorphism group of the quasiaffine variety X' acts on X' infinitely transitively. Also we find wide classes of varieties X admitting such a covering.