{
  "abstract": "We study Borel subgroups of the automorphism group of an affine variety X and their associated Lie algebras. We prove a bijective correspondence between the set of Borel subgroups of Aut(X) and the set of maximal nested unipotent subgroups of Aut(X). We show that if X is factorial of dimension at most 3, then the Lie algebra of every maximal nested unipotent subgroup has the special property of being what we call \"integral\"; we also show that this fails for X = affine space of dimension > 3. As an application of our results, we show that Nagata's automorphism is contained in a unique Borel subgroup.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06664",
  "author_total": 3,
  "authors": [
    {
      "name": "Michael Chitayat"
    },
    {
      "name": "Daniel Daigle"
    },
    {
      "name": "Andriy Regeta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1xxjzm44rp1f9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06664",
  "fulltext_url": null,
  "id": "1xxjzm44rp1f9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06664",
  "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.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220721525",
  "pdf_url": "https://arxiv.org/pdf/2610.06664",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1xxjzm44rp1f9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06664",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06664"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Borel subgroups of the automorphism group of an affine variety",
  "title_text": "Borel subgroups of the automorphism group of an affine variety",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1xxjzm44rp1f9",
  "venue": "arXiv",
  "versions": []
}