Degeneration of tame automorphisms of a polynomial ring

TL;DR

This paper generalizes a recent example of a tame automorphism degenerating into a wild automorphism in a polynomial ring, providing new insights into the structure and behavior of automorphisms.

Contribution

It introduces a new method to generalize the degeneration of tame automorphisms into wild automorphisms in polynomial rings.

Findings

Demonstrates a broader class of tame automorphisms degenerating to wild automorphisms

Provides a novel method for constructing such degenerations

Enhances understanding of automorphism structures in polynomial rings

Abstract

Recently, Edo-Poloni constructed a family of tame automorphisms of a polynomial ring in three variables which degenerates to a wild automorphism. In this note, we generalize the example by a different method.