2022/08/20 by Alexander Perepechko, Perepechko, Alexander, Zaidenberg, Mikhail
Computer Science · Mathematics · #05C60 (secondary) #14J50 #14L30 #14R20 (primary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · doi:10.48550/arxiv.2208.09738
openalex publication_date 2022/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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: given an affine algebraic surface Y, as to when the identity component \rm Aut0 (Y) of the automorphism group \rm Aut (Y) is an algebraic group? We show that this happens if and only if Y admits no effective action of the additive group of the field. In the latter case, \rm Aut0 (Y) is an algebraic torus of rank ≤ 2.