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Abstract: In 2003, Shestakov-Umirbaev solved Nagata-s conjecture on an automorphism ofa polynomial ring. In the present paper, we reconstruct their theory by usingthe -generalized Shestakov-Umirbaev inequality-, which was recently given bythe author. As a consequence, we obtain a more precise tameness criterion forpolynomial automorphisms. In particular, we show that no tame automorphism of apolynomial ring admits a reduction of type IV.



Autor: Shigeru Kuroda

Fuente: https://arxiv.org/







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