{
  "abstract": "Let $f\\colon X\\to X$ be a polarised endomorphism of a complex projective manifold, and let $D\\subset X$ be a reduced totally invariant hypersurface. We prove that every irreducible component of the singular locus of $D$ has codimension one in $D$. In particular, if $D$ is normal, then it is smooth. As an application we prove the linearity of totally invariant divisors for endomorphisms of $\\mathbb P^4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08633",
  "author_total": 2,
  "authors": [
    {
      "name": "Amaël Broustet"
    },
    {
      "name": "Andreas Höring"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/852km6dht2hds.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08633",
  "fulltext_url": null,
  "id": "852km6dht2hds",
  "issns": [],
  "landing_url": "https://hal.science/hal-05745951v1",
  "language": "en",
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "hal",
      "0.math"
    ],
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      "hal",
      "1.math.math-ag"
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      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W7212026921",
  "pdf_url": "https://arxiv.org/pdf/2609.08633",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/852km6dht2hds.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:33Z",
      "native_id": "hal-05745951",
      "source": "hal",
      "url": "https://hal.science/hal-05745951v1"
    },
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08633",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08633"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Singularities of totally invariant hypersurfaces of endomorphisms",
  "title_text": "Singularities of totally invariant hypersurfaces of endomorphisms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/852km6dht2hds",
  "venue": "HAL",
  "versions": []
}