Beschreibung:
A polynomial automorphism F is called shifted linearizable if there exists a linear map L such that LF is linearizable. We prove that the Nagata automorphism N:= (X-YD-ZD2,Y+ZD,Z) where D=XZ+Y2 is shifted linearizable. More precisely, defining a,b,c on its diagonal, we prove that if ac=b2, then L(a,b,c)N is linearizable if and only if bc=|1. We do this as part of a significantly larger theory: for example, any exponent of a homogeneous locally nite derivation is shifted linearizable. We pose the conjecture that the group generated by the linearizable automorphisms may generate the group of automorphisms, and explain why this is a natural question.