Tohoku Mathematical Journal

Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism

Shigeru Kuroda

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Abstract

In 2003, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of a polynomial ring. In the present paper, we reconstruct their theory by using the “generalized Shestakov-Umirbaev inequality”, which was recently given by the author. As a consequence, we obtain a more precise tameness criterion for polynomial automorphisms. In particular, we deduce that no tame automorphism of a polynomial ring admits a reduction of type IV.

Article information

Source
Tohoku Math. J. (2), Volume 62, Number 1 (2010), 75-115.

Dates
First available in Project Euclid: 31 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1270041028

Digital Object Identifier
doi:10.2748/tmj/1270041028

Mathematical Reviews number (MathSciNet)
MR2654304

Zentralblatt MATH identifier
1210.14072

Subjects
Primary: 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
Secondary: 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]

Keywords
Polynomial automorphisms tame generators problem

Citation

Kuroda, Shigeru. Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism. Tohoku Math. J. (2) 62 (2010), no. 1, 75--115. doi:10.2748/tmj/1270041028. https://projecteuclid.org/euclid.tmj/1270041028


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References

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