{
  "abstract": "Let $\\mathscr{X}(\\boldsymbolΣ)$ be the toric Deligne--Mumford stack with stacky torus $\\mathscr{T}$ associated to the stacky fan $\\boldsymbolΣ = (N,Σ, β)$. A toric principal $H$-bundle over $\\mathscr{X}(\\boldsymbolΣ)$ is a principal $H$-bundle $\\mathscr{P}$ equipped with a $\\mathscr{T}$-action lifting the $\\mathscr{T}$-action on $\\mathscr{X}(\\boldsymbolΣ)$, such that the $\\mathscr{T}$-action and the $H$-action on $\\mathscr{P}$ commute. For a connected reductive algebraic group $H$ over $\\mathbb{C}$, we classify the isomorphism classes of framed toric principal $H$-bundles over $\\mathscr{X}(\\boldsymbolΣ)$ in terms of piecewise linear maps from $|Σ|$ to the cone over the Tits building of $H$. Using this classification, we describe the equivariant automorphism group of a toric principal $H$-bundle, and give a necessary and sufficient condition for an equivariant reduction of the structure group. We also show that every toric principal $\\mathrm{GL}(r)$-bundle over the weighted projective stack $\\mathbb{P}(w_0,\\dots,w_n)$ splits equivariantly whenever $r < n$, and that every toric principal $H$-bundle over the weighted stacky projective line $\\mathbb{P}(a,b)$ splits equivariantly when $H$ is a connected reductive algebraic group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33488",
  "author_total": 3,
  "authors": [
    {
      "name": "Ramandeep Singh Arora"
    },
    {
      "name": "Chandranandan Gangopadhyay"
    },
    {
      "name": "Mainak Poddar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44w8kcvgxns5k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33488",
  "fulltext_url": null,
  "id": "44w8kcvgxns5k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33488",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214777040",
  "pdf_url": "https://arxiv.org/pdf/2609.33488",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44w8kcvgxns5k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33488",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33488"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Equivariant principal bundles over toric Deligne--Mumford stacks",
  "title_text": "Equivariant principal bundles over toric Deligne--Mumford stacks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/44w8kcvgxns5k",
  "venue": "arXiv",
  "versions": []
}