{
  "abstract": "We show that the set $A(n, d)$ of polynomial automorphisms $F : \\Bbb C^n \\to \\Bbb C^n$ of degree at most $d$ and with $Jac(F ) = 1$ is Zariski closed. In particular every irreducible component of the set $A(n,d)$ of polynomial mappings with Jacobian $1$ is either composed with polynomial automorphisms or (generically) with counterexamples to the Jacobian Conjecture. Moreover every such component has dimension at least $n^2-1.$ In particular if the set $X(n,d)$ is irreducible, and $n\\ge 3, d\\ge 7$, then a generic element of this set is a counterexample to the Jacobian Conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.20597",
  "author_total": 1,
  "authors": [
    {
      "name": "Zbigniew Jelonek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79jc1nvy0rd8y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.20597",
  "fulltext_url": null,
  "id": "79jc1nvy0rd8y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.20597",
  "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.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7170402445",
  "pdf_url": "https://arxiv.org/pdf/2607.20597",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79jc1nvy0rd8y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2607.20597",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.20597"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On mappings with Jacobian one",
  "title_text": "On mappings with Jacobian one",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/79jc1nvy0rd8y",
  "venue": "arXiv",
  "versions": []
}