Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 62, Number 1 (2010), 75-115.
Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism
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.
Tohoku Math. J. (2), Volume 62, Number 1 (2010), 75-115.
First available in Project Euclid: 31 March 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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