There is no tame automorphism of C^3 with multidegree (4,5,6)

Abstract

It is known that not each triple (d_1,d_2},d_3) of positive integers is a multidegree of a tame automorphism of C^3. In this paper we show that there is no tame automorphism of C^3 with multidegree (4,5,6). To do this we show that there is no pair of polynomials P,Q in C[x,y,z] with certain properties. These properties do not seem particularly restrictive so the non-existence result can be interesting in its own right.