On the DML(1) property for regular endomorphisms of affine spaces: multiplicities of points at infinity
Year: 2026
Type: preprint
Abstract: Let $f$ be a regular endomorphism of $\mathbb{A}_{\mathbb{C}}^N$ of algebraic degree $d$ and let $f_{\infty}$ be the induced endomorphism of the infinity hyperplane $H_{\infty}$. Suppose that for every periodic point $x_0\in H_{\infty}(\mathbb{C})$ of period $n_0$, the geometric mean of the multiplicities $e_{f_{\infty}}(x_0),\dots,e_{f_{\infty}}(f_{\infty}^{n_0-1}(x_0))$ is strictly less than $d$. Then we show that the dynamical Mordell--Lang conjecture for $f$ holds for curves in $\mathbb{A}_{\mathbb{C}}^N$.
Source: arXiv (Cornell University)
Authors: Yang, She, Zheng, Aoyang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G576856182
OpenAlex ID: W7220744133