Abstract:
Invertible polynomial map of the standard 1-parabolic form $x_i \to f_i(x_1,\dots,x_{n-1})$, $i<n$, $x_n\to\alpha x_n+h_n(x_1,\ldots,x_{n-1})$ is a natural generalization of a triangular map. To generalize the previous results about triangular and bitriangular maps, it is shown that the group of tame polynomial transformations $TGA_3$ is generated by an affine group $AGL_3$ and any nonlinear biparabolic map of the form $U_0\cdot q_1\cdot U_1\cdot q_2\cdot U_2,$ where $U_i$ are linear maps and both $q_i$ have the standard 1-parabolic form.
Keywords and phrases:Invertible polynomial map, tame map, affine group, affine Cremona group.
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