Geometrically rational real conic bundles and very transitive actions

TL;DR

This paper investigates the automorphism groups of real algebraic surfaces, characterizing those with very transitive actions and applying these results to classify real algebraic models of compact surfaces, revealing new geometric insights.

Contribution

It provides a characterization of real algebraic surfaces with very transitive automorphism groups and applies this to classify real algebraic models of compact surfaces.

Findings

Identifies conditions for very transitive automorphism groups

Classifies real algebraic models of compact surfaces

Reveals new geometric properties of real loci

Abstract

In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.