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摘要翻译：
设X是特征为零的代数闭域k上的仿射不可约簇。给定一个自同构F，我们用k(X)^F表示它的不变量域，即X上的有理函数F的集合，使得F(F)=F。设n(F)是k(X)^F对k的超越度。本文研究了X的自同构类F,其中n(F)=dim x-1。更确切地说，我们证明了在X上的某些条件下，每一个这样的自同构都是F=A_G的形式，其中A是维数为1的线性代数群G在X上的代数作用，其中G属于G。作为应用，我们确定了n(F)=1的平面自同构的共轭类。
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英文标题：
《On algebraic automorphisms and their rational invariants》
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作者：
Philippe Bonnet
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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：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 X be an affine irreducible variety over an algebraically closed field k of characteristic zero. Given an automorphism F, we denote by k(X)^F its field of invariants, i.e. the set of rational functions f on X such that f(F)=f. Let n(F) be the transcendence degree of k(X)^F over k. In this paper, we study the class of automorphisms F of X for which n(F)= dim X - 1. More precisely, we show that under some conditions on X, every such automorphism is of the form F=A_g, where A is an algebraic action of a linear algebraic group G of dimension 1 on X, and where g belongs to G. As an application, we determine the conjugacy classes of automorphisms of the plane for which n(F)=1.
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PDF链接：
https://arxiv.org/pdf/0704.1588
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