The group of automorphisms of a real rational surface is n-transitive

TL;DR

This paper proves that the automorphism group of a real rational surface acts n-transitively for all n, and uses this to simplify the classification of such surfaces by their topology.

Contribution

It establishes the n-transitivity of the automorphism group on real rational surfaces for all n, providing a new proof of their topological classification.

Findings

Aut(X) acts n-transitively for all n

Simplified proof of surface isomorphism classification

Automorphism group properties linked to topological equivalence

Abstract

Let X be a rational nonsingular compact connected real algebraic surface. Denote by Aut(X) the group of real algebraic automorphisms of X. We show that the group Aut(X) acts n-transitively on X, for all natural integers n. As an application we give a new and simpler proof of the fact that two rational nonsingular compact connected real algebraic surfaces are isomorphic if and only if they are homeomorphic as topological surfaces.