标题： 谢斯塔科夫-乌米尔巴耶夫约简与多项式自同构的纳加塔猜想 显示英文标题

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

摘要： 2003年，Shestakov-Umirbaev解决了Nagata关于多项式环自同构的猜想。 在本文中，我们通过使用作者最近提出的“广义Shestakov-Umirbaev不等式”来重建他们的理论。 作为结果，我们得到了一个更精确的多项式自同构的良态准则。 特别是，我们证明了多项式环的任何良态自同构都不允许类型IV的约简。 显示英文摘要

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.