Locally tame plane polynomial automorphisms

2010/11/03 by Joost Berson, Berson, Joost, Adrien Dubouloz +5
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.1011.0976

arxiv created 2010/11/03 · openalex publication_date 2010/11/03 · arxiv updated 2010/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For automorphisms of a polynomial ring in two variables over a domain R, we show that local tameness implies global tameness provided that every 2-generated invertible R-module is free. We give many examples illustrating this property.

Related

• Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring
• A non-tame and non-co-tame automorphism of the polynomial ring
• A new co-tame automorphism of the polynomial ring
• Generalisations of the tame automorphisms over a domain of positive characteristic
• Degeneration of tame automorphisms of a polynomial ring