射影直线上动力系统的Chow商模空间与重标度极限
Chow Quotient Moduli Space of Dynamical Systems on the Projective Line and Rescaling Limits
浏览论文内容
中文总结 AI 辅助
本文研究射影直线上次数为d的有理自映射模空间的Chow商紧化，计算三维轨道环度数，引入带标记Chow商记录重标度极限，并扩展不动点乘子映射。
中文摘要 AI 辅助
我们研究了射影直线上次数为$d$的有理自映射的模空间的Chow商紧化。我们计算了Clebsch--Gordan紧化中每个三维轨道环的度数，用主分量和洞深度来表示。作为推论，我们得到了一般轨道类以及由迭代诱导的Chow商上的有理映射。我们还引入了一个带标记的Chow商，旨在记录重标度极限的集合，用装饰树来描述它，并将不动点乘子映射扩展到未标记Chow商的规范化。
英文摘要
We study Chow-quotient compactifications of the moduli space of degree-$d$ rational self-maps of the projective line. We compute the degree of every three-dimensional orbit cycle in the Clebsch--Gordan compactification in terms of the main component and the hole depths. As consequences, we obtain the generic orbit class and a rational map on Chow quotients induced by iteration. We also introduce a marked Chow quotient designed to record collections of rescaling limits, describe it by decorated trees, and extend the fixed-point multiplier map to the normalization of the unmarked Chow quotient.
