{
  "abstract": "We study the automorphism ind-group of a Stanley-Reisner variety $X_Δ$ through a combinatorial toolkit on the underlying complex: a facet closure operator, its Demazure roots, and the resulting dichotomy between exposed and hidden facets. Our main theorem is that a fully exposed complex, that is, one in which every facet has a private vertex, is recovered from the ind-group: $\\mathrm{Aut}(X_Δ)\\cong\\mathrm{Aut}(X_{Δ'})$ forces $Δ\\congΔ'$. The hypothesis cannot be dropped, but it holds after one stabilization, so for arbitrary $Δ,Δ'$ an isomorphism $\\mathrm{Aut}(X_Δ\\times\\mathbb{A}^1)\\cong\\mathrm{Aut}(X_{Δ'}\\times\\mathbb{A}^1)$ already forces $Δ\\congΔ'$. At the opposite extreme, a fully hidden $Δ$ gives $\\mathrm{Aut}(X_Δ)=T_0\\rtimes S(Δ)$, never isomorphic to the ind-group of a non-rigid Stanley-Reisner variety. The criterion decides graphs and skeleta, and every complex is homotopy equivalent to a fully exposed one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02785",
  "author_total": 2,
  "authors": [
    {
      "name": "Roberto Díaz"
    },
    {
      "name": "José Alejandro Samper"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cw2vhvq6mkqww.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02785",
  "fulltext_url": null,
  "id": "cw2vhvq6mkqww",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02785",
  "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": "W7207596778",
  "pdf_url": "https://arxiv.org/pdf/2609.02785",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cw2vhvq6mkqww.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02785",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02785"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Characterization of Stanley-Reisner varieties by their automorphism group",
  "title_text": "Characterization of Stanley-Reisner varieties by their automorphism group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/cw2vhvq6mkqww",
  "venue": "arXiv",
  "versions": []
}