Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735
SHESTAKOV-UMIRBAEV REDUCTIONS AND NAGATA'S CONJECTURE ON A POLYNOMIAL AUTOMORPHISM
SHIGERU KURODA
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ジャーナル フリー

2010 年 62 巻 1 号 p. 75-115

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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.
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