Coordinates of R[x,y]: Constructions and classifications
Abstract
Let R be a PID. We construct and classify all coordinates of R[x,y] of the form p2y+Q2(p1x+Q1(y)) with p1 and p2 in qt(R) and Q1 and Q2 in qt(R)[y]. From this construction (with R=K[z]) we obtain non tame automorphisms s of K[x,y,z] (where K is a field of characteristic 0) such that the sub-group generated by s and the affine automorphisms contains all tame automorphisms.
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