Tohoku Mathematical Journal
2010
March
SECOND SERIES VOL. 62, NO. 1

Tohoku Math. J.
62 (2010), 75-115

Title SHESTAKOV-UMIRBAEV REDUCTIONS AND NAGATA'S CONJECTURE ON A POLYNOMIAL AUTOMORPHISM

Dedicated to the memory of Professor Masayoshi Nagata
Author Shigeru Kuroda

(Received October 9, 2008, revised October 13, 2009)
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.

2000 Mathematics Subject Classification. Primary 14R10; Secondary 13F20.
Key words and phrases. Polynomial automorphisms, tame generators problem.

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