{
  "abstract": "Fix integers $k,d\\geq2$. Let $\\mathrm{End}_d^k$ denote the parameter space of endomorphisms of $\\mathbb{P}^k$ of algebraic degree $d$. We prove that there exists a dense Zariski open subset $U_{d,k}\\subset\\mathrm{End}_d^k$, defined over $\\mathbb{Q}$, such that, for every $f\\in U_{d,k}(\\mathbb{C})$, every dominant rational self-map of $\\mathbb{P}^k$ commuting with an iterate of $f$ is itself an iterate of $f$. The key intermediate result classifies dominant rational semiconjugacies to iterates of $f$ from normal projective varieties of dimension $k$. The proof uses finite-level monodromy and its action on the rooted preimage tree of a point outside the branch locus of an iterate of $f$. An analogous centralizer theorem holds generically for regular polynomial endomorphisms of $\\mathbb{C}^k$. These results extend several theorems of Pakovich to higher dimensions. We give two applications. We first classify periodic dominant correspondences between a general endomorphism and an arbitrary endomorphism of degree at least two. We then show that, for a general $f\\in\\mathrm{End}_d^k$, an irreducible hypersurface of $\\mathbb{P}^k$ is $f$-special in the sense of Ghioca--Tucker and DeMarco--Mavraki if and only if it is $f$-preperiodic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09858",
  "author_total": 1,
  "authors": [
    {
      "name": "Yugang Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0arnyq0y2jrpr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09858",
  "fulltext_url": null,
  "id": "0arnyq0y2jrpr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09858",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7212127753",
  "pdf_url": "https://arxiv.org/pdf/2609.09858",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0arnyq0y2jrpr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.09858",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09858"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "A general endomorphism of $\\mathbb{P}^k$ has trivial iterated centralizer",
  "title_text": "A general endomorphism of ℙ^k has trivial iterated centralizer",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/0arnyq0y2jrpr",
  "venue": "arXiv",
  "versions": []
}