The automorphism group of a rational projective k*-surface

2020/10/13 by Juergen Hausen, Hausen, Juergen, Timo Hummel +1
Mathematics · #14J26 #14L30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2010.06414

openalex publication_date 2020/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Automorphisms of Finite Order on Rational Surfaces
• Rational surfaces with a large group of automorphisms
• Rational surfaces with a non-arithmetic automorphism group
• The group of automorphisms of a real rational surface is n-transitive
• Groups acting on cubic surfaces in characteristic zero