{
  "abstract": "In this note, we show that over a geometrically irreducible smooth projective curve over an infinite field $k$, the moduli stack of semistable vector bundles of fixed determinant is $\\mathbb{A}^1$-connected if and only if the moduli stack admits a $k$-rational point. For this we use Langton's elementary modifications for vector bundles at the level of families. In addition, we prove the $\\mathbb{A}^1$-connectedness of the moduli stack of symplectic bundles with forms valued in a fixed line bundle $L$ on a smooth projective curve of genus $g \\ge 2$ over an infinite field $k$ with $C(k)\\neq \\emptyset$. As an application, we deduce the $\\mathbb{A}^1$-connectedness of moduli stack of quasi-parabolic symplectic vector bundles with forms valued in a fixed line bundle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06458",
  "author_total": 2,
  "authors": [
    {
      "name": "Umesh V Dubey"
    },
    {
      "name": "Rakesh Pawar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5nch3ymdv5n6p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06458",
  "fulltext_url": null,
  "id": "5nch3ymdv5n6p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06458",
  "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": "W7220694290",
  "pdf_url": "https://arxiv.org/pdf/2610.06458",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5nch3ymdv5n6p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06458",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06458"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "$\\mathbb{A}^1$-connectedness of moduli of semistable bundles and symplectic bundles on a curve",
  "title_text": "𝔸^1-connectedness of moduli of semistable bundles and symplectic bundles on a curve",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/5nch3ymdv5n6p",
  "venue": "arXiv",
  "versions": []
}