{
  "abstract": "A Demazure model of an algebraic $k$-torus $T$ split by a finite Galois extension of fields $L/k$ and splitting group $G=\\text{Gal}(L/k)$ is a smooth projective $T_L$-toric variety $X_Σ$ such that the natural action of $G$ on $T_L$ extends to $X_Σ$. A smooth projective model of the algebraic $k$-torus $T$ can then be taken to be the quotient of a Demazure model by its splitting group. The existence of Demazure models of algebraic $k$-tori was determined by Brylinski and further refined by Colliot-Thélène, Harari and Skorobogatov. Voskresenskii and Kunyavskii's birational classifications of algebraic $k$-tori in dimensions 2 and 3 involved constructions of Demazure models of the algebraic $k$-tori corresponding to maximal finite subgroups of $\\text{GL}(r,\\mathbb{Z})$ for $r=2,3$. We discuss some explicit constructions of Demazure models of algebraic $k$-tori, making connections with the defining integral representations of their splitting groups. The constructions determine smooth projective Demazure models of the algebraic tori corresponding to maximal finite subgroups of $\\text{GL}(4,\\mathbb{Z})$. Since projective toric varieties are determined by lattice polytopes, our constructions focus on some highly symmetric families of polytopes, such as root polytopes and central transportation polytopes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30482",
  "author_total": 1,
  "authors": [
    {
      "name": "Nicole Lemire"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7at1e4tw2wejj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30482",
  "fulltext_url": null,
  "id": "7at1e4tw2wejj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30482",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214614410",
  "pdf_url": "https://arxiv.org/pdf/2609.30482",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7at1e4tw2wejj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30482",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30482"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Demazure Models of Algebraic Tori in Dimension 4",
  "title_text": "Demazure Models of Algebraic Tori in Dimension 4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/7at1e4tw2wejj",
  "venue": "arXiv",
  "versions": []
}