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摘要翻译：
设$i$是定义$k^n$自同构的多项式的导项之间关系的理想。本文证明了保$I$的局部幂零导子的存在性。此外，如果$I$是主体，即$I=(R)$,我们计算了由自同构定义的某个度函数$\deg2$的一个上界$\deg2(R)$。作为应用，我们确定了$k^3$自同构关系的所有主理想，并给出了关于$k^{2}$自同构驯化性的Jung-van der Kulk定理的两个初等证明。
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英文标题：
《Relations between the leading terms of a polynomial automorphism》
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作者：
Philippe Bonnet and St\'ephane V\'en\'ereau
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最新提交年份：
2008
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分类信息：
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：
Let $I$ be the ideal of relations between the leading terms of the polynomials defining an automorphism of $K^n$. In this paper, we prove the existence of a locally nilpotent derivation which preserves $I$. Moreover, if $I$ is principal, i.e. $I=(R)$, we compute an upper bound for $\deg_2(R)$ for some degree function $\deg_2$ defined by the automorphism. As applications, we determine all the principal ideals of relations for automorphisms of $K^3$ and deduce two elementary proofs of the Jung-van der Kulk Theorem about the tameness of automorphisms of $K^{2}$.
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PDF链接：
https://arxiv.org/pdf/0808.1821
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