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.
Citation
Shigeru Kuroda. "Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism." Tohoku Math. J. (2) 62 (1) 75 - 115, 2010. https://doi.org/10.2748/tmj/1270041028
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