{
  "abstract": "Let $\\mathfrak{C}$ be a projective stacky curve over an infinite field $k$ with the coarse space $C$, a geometrically connected smooth projective curve, together with a generating sheaf $\\mathcal{E}$ on $\\mathfrak{C}$. We consider the moduli stack of $\\mathcal{E}$-semistable vector bundles of fixed determinant and multiplicities on $\\mathfrak{C}$, and show that it is $\\mathbb{A}^1$-connected if and only if it admits a $k$-rational point. We show that this holds whenever genus of $C$ is at least $2$ and $C(k)\\neq \\emptyset$. As a consequence, we conclude that, for any system of weights $\\boldsymbolα$, the moduli stack of parabolic $\\boldsymbolα$-semistable vector bundles of fixed determinant and quasi-parabolic data on a geometrically connected smooth projective curve is $\\mathbb{A}^1$-connected.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28203",
  "author_total": 3,
  "authors": [
    {
      "name": "Sujoy Chakraborty"
    },
    {
      "name": "Saurav Holme Choudhury"
    },
    {
      "name": "Rakesh Pawar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/93v2r3gqsrzyc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28203",
  "fulltext_url": null,
  "id": "93v2r3gqsrzyc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28203",
  "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": "W7214226018",
  "pdf_url": "https://arxiv.org/pdf/2609.28203",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/93v2r3gqsrzyc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2609.28203",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28203"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "$\\mathbb{A}^1$-connectedness of moduli of vector bundles on a stacky curve",
  "title_text": "𝔸^1-connectedness of moduli of vector bundles on a stacky curve",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/93v2r3gqsrzyc",
  "venue": "arXiv",
  "versions": []
}