{
  "abstract": "Let $f$ be a dominant rational self-map of a normal projective variety over an algebraically closed field of arbitrary characteristic, or a dominant meromorphic self-map of a compact Kähler manifold. We prove that in every codimension, the degree sequence of $f$ differs from its dynamical-degree growth by at most a polynomial factor, with an explicit universal bound on the polynomial exponent. In particular, subexponential but superpolynomial degree growth cannot occur. At a strict dynamical-degree break, we prove the sharper asymptotic \\[ \\mathrm{deg}_{i,ω}(f^n)=C_{f,ω,i}\\,λ_i(f)^n+O(η^n), \\] for every $\\sqrt{λ_{i-1}(f)λ_{i+1}(f)}<η<λ_i(f)$. This extends the degree-asymptotic theorem of Dang--Favre from codimension one in characteristic zero to arbitrary codimension and arbitrary characteristic, and recovers the surface theorem of Boucksom--Favre--Jonsson. Both results rely on a uniform estimate for the temporal discrete logarithmic Laplacian of the degree sequences, obtained by applying the Ptolemy inequality to ordered Hodge--Lorentz packages on varying finite-time orbit spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18094",
  "author_total": 1,
  "authors": [
    {
      "name": "Fei Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5wftva0146ys6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18094",
  "fulltext_url": null,
  "id": "5wftva0146ys6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18094",
  "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"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221771940",
  "pdf_url": "https://arxiv.org/pdf/2610.18094",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5wftva0146ys6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.18094",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18094"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Degree growth of rational and meromorphic self-maps",
  "title_text": "Degree growth of rational and meromorphic self-maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/5wftva0146ys6",
  "venue": "arXiv",
  "versions": []
}