周期一与周期二乘子的有理映射的通用重构
Generic reconstruction of rational maps from multipliers of periods one and two
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中文总结 AI 辅助
本文证明对任意次数d≥2且特征非2的域，模空间上由周期一、二乘子构成的谱态射双有理于其像闭包，从而在代数闭域上通用单射，证实了Ji-Xie猜想，方法涉及正规形、非阿基米德退化与对不变量重构。
中文摘要 AI 辅助
对于每个整数$d\geq2$以及每个特征不等于$2$的域，我们证明了在次数为$d$的有理映射的模空间$\mathcal{M}_d$上，由周期一和周期二的周期点构成的乘子谱态射是双有理于其像的闭包。因此，在特征不等于$2$的每个代数闭域上，该态射是通用单射的，这证明了Ji和Xie在特征零情形下的一个近期猜想。证明使用了固定指标正规形、二周期的非阿基米德退化，以及从对不变量对仿射不动点构型进行双有理重构。
英文摘要
For every integer $d\geq2$ and every field of characteristic different from $2$, we prove that on the moduli space $\mathcal{M}_d$ of degree-$d$ rational maps, the multiplier spectrum morphism formed from the periodic points of periods one and two is birational to the closure of its image. Consequently, over every algebraically closed field of characteristic different from $2$, it is generically injective, which proves a recent conjecture of Ji and Xie in characteristic zero. The proof uses a fixed-index normal form, a non-archimedean degeneration of two-cycles, and birational reconstruction of an affine fixed-point configuration from pair invariants.
发表机构
- School of Mathematical Sciences, Peking University（北京大学数学科学学院）
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