The automorphism group of a rational projective k*-surface

TL;DR

This paper explicitly describes the automorphism group of possibly singular rational projective k*-surfaces, characterizes almost homogeneous cases, and details the acting groups and homogeneous spaces.

Contribution

It provides an explicit description of the automorphism group for singular rational projective k*-surfaces and characterizes almost homogeneous cases.

Findings

Explicit description of the automorphism group in terms of isotropy groups and intersection numbers.

Characterization of almost homogeneous rational projective k*-surfaces.

Identification of two-dimensional groups acting almost transitively.

Abstract

We consider possibly singular rational projective k*-surfaces and provide an explicit description of the unit component of the automorphism group in terms of isotropy group orders and intersection numbers of suitable invariant curves. As an application, we characterize the almost homogeneous rational projective k*-surfaces and we specify the two-dimensional groups acting almost transitively as well as the corresponding homogeneous spaces.