Locally tame plane polynomial automorphisms

TL;DR

This paper investigates when locally tame polynomial automorphisms in two variables over a domain are globally tame, establishing conditions related to the freeness of certain modules and providing illustrative examples.

Contribution

It proves that local tameness implies global tameness under the condition that all 2-generated invertible modules over the domain are free, extending understanding of polynomial automorphisms.

Findings

Local tameness implies global tameness under specific module conditions

Many examples illustrating the property of local versus global tameness

Conditions on invertible modules are crucial for tameness equivalence

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.