An Automorphism group of a rational surface: Not too big not too small

2022/02/24 by Kyounghee Kim, Kim, Kyounghee
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2202.12354

openalex publication_date 2022/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article concerns the realization problem of subgroups of Coxeter groups. We construct a subgroup G of the Coxeter group W₁₅ such that G is realized as automorphism groups of a rational surface X and G ≅ Aut(X)^* ≅ D₃ × ℤ. We also show that there is an element ω in W₁₄ is not realizable.

Related

• Rational surfaces with a large group of automorphisms
• The Dynamical Degrees of Rational Surface Automorphisms
• Affine surfaces with a huge group of automorphisms
• The automorphism group of a rational projective k*-surface
• Coxeter groups, Lorentzian lattices, and K3 surfaces