摘要翻译：
最近，Shestakov-Umirbaev解决了关于多项式环的自同构的Nagata猜想。为了解决这个猜想，他们为多项式环的自同构定义了称为I-IV型约化的概念。Shestakov-Umirbaev首先发现了一个承认I型约简的自同构。van den Essen-Makar-Limanov-Willems用计算机给出了一族这样的自同构。本文利用局部幂零导子构造了这类自同构。因此，我们发现存在一个自同构，允许对每个可能值满足一定程度条件的I型约简。
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英文标题：
《Automorphisms of a polynomial ring which admit reductions of type I》
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作者：
Shigeru Kuroda
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Commutative Algebra        交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  Recently, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of a polynomial ring. To solve the conjecture, they defined notions called reductions of types I--IV for automorphisms of a polynomial ring. An automorphism admitting a reduction of type I was first found by Shestakov-Umirbaev. Using a computer, van den Essen--Makar-Limanov--Willems gave a family of such automorphisms. In this paper, we present a new construction of such automorphisms using locally nilpotent derivations. As a consequence, we discover that there exists an automorphism admitting a reduction of type I which satisfies some degree condition for each possible value.
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PDF链接：
https://arxiv.org/pdf/0708.2120