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Tohoku Mathematical Journal
SECOND SERIES VOL. 62, NO. 1
|Tohoku Math. J.|
62 (2010), 75-115
SHESTAKOV-UMIRBAEV REDUCTIONS AND NAGATA'S CONJECTURE ON A POLYNOMIAL AUTOMORPHISM
Dedicated to the memory of Professor Masayoshi Nagata
(Received October 9, 2008, revised October 13, 2009)
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.
2000 Mathematics Subject Classification.
Primary 14R10; Secondary 13F20.
Key words and phrases.
Polynomial automorphisms, tame generators problem.
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