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PreprintCC BY 4.0arXiv

On the DML(1) property for regular endomorphisms of affine spaces: multiplicities of points at infinity

  • She Yang
  • Aoyang Zheng
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Abstract

Let f be a regular endomorphism of 𝔸ℂN of algebraic degree d and let f∞ be the induced endomorphism of the infinity hyperplane H∞. Suppose that for every periodic point x0∈ H∞(β„‚) of period n0, the geometric mean of the multiplicities ef∞(x0),…,ef∞(f∞n0βˆ’1(x0)) is strictly less than d. Then we show that the dynamical Mordell--Lang conjecture for f holds for curves in 𝔸ℂN.

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Cite

BibTeXRIS
BibTeX
@misc{yang2026dml1,
  title = {{On the DML(1) property for regular endomorphisms of affine spaces: multiplicities of points at infinity}},
  author = {She Yang and Aoyang Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05850},
  eprint = {2610.05850},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05850},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the DML(1) property for regular endomorphisms of affine spaces: multiplicities of points at infinity
AU  - She Yang
AU  - Aoyang Zheng
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05850
UR  - https://arxiv.org/abs/2610.05850
AB  - Let f be a regular endomorphism of 𝔸_β„‚^N of algebraic degree d and let f_∞ be the induced endomorphism of the infinity hyperplane H_∞. Suppose that for every periodic point x_0∈ H_∞(β„‚) of period n_0, the geometric mean of the multiplicities e_f_∞(x_0),…,e_f_∞(f_∞^n_0βˆ’1(x_0)) is strictly less than d. Then we show that the dynamical Mordell--Lang conjecture for f holds for curves in 𝔸_β„‚^N.
ER  -