There is no tame automorphism of C^3 with muldidegree (3,4,5)

TL;DR

This paper proves that no tame automorphism of complex three-dimensional space has multidegree (3,4,5), addressing a specific case in the broader problem of characterizing automorphisms by their multidegrees.

Contribution

The paper establishes the non-existence of tame automorphisms with multidegree (3,4,5) in C^3, advancing understanding of automorphism structures.

Findings

No tame automorphism of C^3 has multidegree (3,4,5)

Provides partial classification of automorphisms by multidegree

Contributes to the problem of characterizing polynomial automorphisms

Abstract

Let F=(F_1,...,F_n):C^n --> C^n be any polynomial mapping. By multidegree of F, denoted mdeg F, we call the sequence of positive integers (deg F_1,...,F_n). In this paper we addres the following problem: for which sequence (d_1,...,d_n) there is an automorphism or tame automorphism F:C^n --> C^n with mdeg F=(d_1,...,d_n}. We proved, among other things, that there is no tame automorphism F:C^3 --> C^3 with mdeg F=(3,4,5).