Degeneration of Tame Automorphisms of a Polynomial Ring

Abstract

Recently, Edo and 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.

Key Words:

• Degeneration
• Ind-group
• Polynomial automorphism
• Tame subgroup

2010 Mathematics Subject Classification:

• Primary: 14R10
• Secondary: 13N15

ACKNOWLEDGMENTS

The first version of this note was written for a discussion at Saitama University in 2014. Thanks are due to the participants, especially to Prof. E. Edo for introducing this topic, and to Prof. A. Dubouloz for the suggestion of generalizing R which was originally a multivariate polynomial ring.