Shestakov-Umirbaev约化与Nagata关于多项式自同构的猜想
Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism
摘要：
2003年，Shestakov-Umirbaev解决了Nagata关于多项式环的自同构的猜想。本文利用作者最近提出的“广义Shestakov-Umirbaev不等式”，重建了他们的理论。作为结果，我们得到一个更精确的驯服准则多项式自同构。特别是，我们表明，没有驯服的自同构的多项式环承认减少IV型。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
