{
  "abstract": "Let $K$ be a number field or a function field of a curve. Let $f$ be a dominant rational self-map of a normal projective variety $X$ of dimension $d$ over $K$, and let $h_H\\geq1$ be an ample Weil height. Let $λ_1(f)$ denote the first dynamical degree of $f$. We show that there is a constant $C_{f,h_H}>0$ such that, for any $n\\geq1$ and any point $P\\in X(\\overline{K})$ with well-defined forward orbit, $h_H(f^n(P))\\leq C_{f,h_H}h_H(P)n^{2(d-1)}λ_1(f)^n$ if $λ_1(f)>1$, and $h_H(f^n(P))\\leq C_{f,h_H}h_H(P)n^{2d}$ if $λ_1(f)=1$. Over number fields, the proof combines a new uniform upper bound for arithmetic degrees with a uniform comparison of point heights. Over function fields, it relies on the corresponding uniform upper bound for geometric degrees on a projective model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33570",
  "author_total": 2,
  "authors": [
    {
      "name": "Fei Hu"
    },
    {
      "name": "Jiarui Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3wesfm77d0e78.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33570",
  "fulltext_url": null,
  "id": "3wesfm77d0e78",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33570",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223943837",
  "pdf_url": "https://arxiv.org/pdf/2610.33570",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3wesfm77d0e78.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33570",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33570"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Height growth of rational self-maps",
  "title_text": "Height growth of rational self-maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3wesfm77d0e78",
  "venue": "arXiv",
  "versions": []
}