{
  "abstract": "We classify complete toric threefolds $X$ such that the automorphism group $\\text{Aut}(X)$ acts on $X$ with an open orbit whose complement does not contain a divisor. The latter condition means that for any ray $ρ$ of the fan $Σ_X$ there is a Demazure root of $Σ_X$ associated with $ρ$. We also find among these varieties those $X$ for which the group $\\text{Aut}(X)$ is transitive on the smooth locus $X^{\\text{reg}}$. The classifications are based on Gale-dual interpretations of these properties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09051",
  "author_total": 2,
  "authors": [
    {
      "name": "Ivan Arzhantsev"
    },
    {
      "name": "Kirill Shakhmatov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7pdb6fqn4kbdj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09051",
  "fulltext_url": null,
  "id": "7pdb6fqn4kbdj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09051",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7212055957",
  "pdf_url": "https://arxiv.org/pdf/2609.09051",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7pdb6fqn4kbdj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.09051",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09051"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Automorphisms of toric varieties and Gale duality",
  "title_text": "Automorphisms of toric varieties and Gale duality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/7pdb6fqn4kbdj",
  "venue": "arXiv",
  "versions": []
}