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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, Number 1, Pages 34–39 (Mi basm149)  

Research articles

Generating properties of biparabolic invertible polynomial maps in three variables

Yu. Bodnarchuk

University "Kiev Mohyla Academy", Kyiv, Ukraine

Abstract: Invertible polynomial map of the standard 1-parabolic form $x_i \to f_i(x_1,…,x_{n-1})$, $i<n$, $x_n\to\alpha x_n+h_n(x_1,\ldots,x_{n-1})$ 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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MSC: 14E07
Received: 23.09.2003
Language: English

Citation: Yu. Bodnarchuk, “Generating properties of biparabolic invertible polynomial maps in three variables”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, no. 1, 34–39

Citation in format AMSBIB
\Bibitem{Bod04}
\by Yu.~Bodnarchuk
\paper Generating properties of biparabolic invertible polynomial maps in three variables
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2004
\issue 1
\pages 34--39
\mathnet{http://mi.mathnet.ru/basm149}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2097594}
\zmath{https://zbmath.org/?q=an:1076.14083}


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