There is no tame automorphism of $\mathbb {C}^{3}$ with multidegree $(3,4,5)$
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- by Marek Karaś PDF
- Proc. Amer. Math. Soc. 139 (2011), 769-775 Request permission
Abstract:
Let $F=(F_{1},\ldots ,F_{n}):\mathbb {C}^{n}\rightarrow \mathbb {C}^{n}$ be any polynomial mapping. The multidegree of $F$, denoted $\textrm {mdeg} F,$ is the sequence of positive integers $(\deg F_{1},\ldots ,\deg F_{n}).$ In this paper we address the following problem: for which sequence $(d_{1},\ldots ,d_{n})$ is there an automorphism or a tame automorphism $F:\mathbb {C}^{n}\rightarrow \mathbb {C}^{n}$ with $\textrm {mdeg} F=(d_{1},\ldots ,d_{n})$? We prove, among other things, that there is no tame automorphism $F:\mathbb {C}^{3}\rightarrow \mathbb {C}^{3}$ with $\textrm {mdeg} F=(3,4,5)$.References
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Additional Information
- Marek Karaś
- Affiliation: Instytut Matematyki, Uniwersytetu Jagiellońskiego, ul. Łojasiewicza 6, 30-348 Kraków, Poland
- Email: Marek.Karas@im.uj.edu.pl
- Received by editor(s): February 24, 2009
- Published electronically: November 10, 2010
- Communicated by: Ted Chinburg
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 769-775
- MSC (2010): Primary 14Rxx, 14R10
- DOI: https://doi.org/10.1090/S0002-9939-2010-10779-7
- MathSciNet review: 2745629