Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism

Details Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism

2007-12-30

arxiv.org/abs/0801.0117v2

Mathematics

Commutative Algebra

52 pages

Scientific paper

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 show that no tame automorphism of a polynomial ring admits a reduction of type IV.

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