Tame and Wild Coordinates of $K[z][x,y]$
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- by Vesselin Drensky and Jie-Tai Yu PDF
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Abstract:
Let $K$ be a field of characteristic zero. We characterize coordinates and tame coordinates in $K[z][x,y]$, i.e. the images of $x$ respectively under all automorphisms and under the tame automorphisms of $K[z][x,y]$. We also construct a new large class of wild automorphisms of $K[z][x,y]$ which maps $x$ to a concrete family of nice looking polynomials. We show that a subclass of this class is stably tame, i.e. becomes tame when we extend its automorphisms to automorphisms of $K[z][x,y,t]$.References
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Additional Information
- Vesselin Drensky
- Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria
- MR Author ID: 59730
- Email: drensky@math.bas.bg
- Jie-Tai Yu
- Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
- Email: yujt@hkusua.hku.hk
- Received by editor(s): March 11, 1999
- Published electronically: October 19, 2000
- Additional Notes: The research of the first author was partially supported by Grant MM605/96 of the Bulgarian Foundation for Scientific Research.
The research of the second author was partially supported by RGC Grant HKU7126-98P and CRCG Grant 10201869.23067.25500.302.01 - © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 519-537
- MSC (2000): Primary 13B25; Secondary 13B10, 13P10, 14E07
- DOI: https://doi.org/10.1090/S0002-9947-00-02617-9
- MathSciNet review: 1709773