On face polynomials
For a \({\mathbb{C}}\)-automorphism of \({\mathbb{C}}[X,Y]\) given by \(X\mapsto f\), \(Y\mapsto g\), the four polynomials f(0,t), g(0,t), f(t,0), g(t,0) are called its \textit{face polynomials}. The last two authors have proved earlier [J. Pure Appl. Algebra 40, 245-257 (1986; Zbl 0622.13003) and ibid. 52, No.1/2, 103-119 (1988)] that the face polynomials determine the automorphism and have given some conditions necessary for a set of four polynomials to be the face polynomials of an automorphisms. In this paper these conditions are proved to be also sufficient.
scientific article; zbMATH DE number 4067060