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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $\textrm {mdeg} F=(3,4,5)$.
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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