Automorphism groups of rigid affine surfaces: The identity component
Abstract
It is known that the identity component of the automorphism group of a projective algebraic variety is an algebraic group.This is not true in general for quasi-projective varieties.In this note, we address the question as to when, given an affine algebraic surface Y , the identity component Aut • (Y ) of the automorphism group Aut(Y ) is an algebraic group.We show that this occurs if and only if Y admits no effective action of the additive group G a of the field.In the latter case, Aut • (Y ) is an algebraic torus of rank at most 2.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Polynomial and algebraic computation
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Algebraic geometry
- Publisher
- Foundation Compositio Mathematica
- Pages
- 667–704
- Publication date
- 21 August 2026
- Language
- EN