PreprintCC BY 4.0arXiv
On the DML(1) property for regular endomorphisms of affine spaces: the 𝔾m-case
Abstract
Let f be a regular endomorphism of 𝔸ℂN and let C⊆𝔸ℂN be an irreducible curve. Suppose C has an infinite intersection with the f-orbit of a point x∈𝔸N(ℂ). Then the normalization of C is isomorphic to either 𝔸1 or 𝔾m. We prove that C is f-periodic in the latter case, as expected by the dynamical Mordell-Lang conjecture.
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BibTeX
@misc{yang2026dml1,
title = {{On the DML(1) property for regular endomorphisms of affine spaces: the $\mathbbG_m$-case}},
author = {She Yang and Aoyang Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29107},
eprint = {2609.29107},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29107},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the DML(1) property for regular endomorphisms of affine spaces: the 𝔾_m-case
AU - She Yang
AU - Aoyang Zheng
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29107
UR - https://arxiv.org/abs/2609.29107
AB - Let f be a regular endomorphism of 𝔸_ℂ^N and let C⊆𝔸_ℂ^N be an irreducible curve. Suppose C has an infinite intersection with the f-orbit of a point x∈𝔸^N(ℂ). Then the normalization of C is isomorphic to either 𝔸^1 or 𝔾_m. We prove that C is f-periodic in the latter case, as expected by the dynamical Mordell-Lang conjecture.
ER -