{
  "abstract": "We prove a Torelli theorem for full moduli stacks of vector bundles of rank at least three with fixed determinant on a smooth, proper, geometrically connected, tame Deligne--Mumford curve of coarse genus at least two over an arbitrary field $k$. We also prove a Torelli theorem for the full moduli stack of vector bundles of rank at least three of fixed-degree under an explicit compatibility hypothesis. The method is intrinsic to the stack: faithful special-linear linearizations recover Picard stacks, and determinants of tangent complexes recover the canonical principal polarization. This is the first part in a series of two papers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29011",
  "author_total": 3,
  "authors": [
    {
      "name": "Soham Ghosh"
    },
    {
      "name": "Ting Gong"
    },
    {
      "name": "Max Lieblich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bbkfdps8qv5z6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29011",
  "fulltext_url": null,
  "id": "bbkfdps8qv5z6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29011",
  "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": "W7214303677",
  "pdf_url": "https://arxiv.org/pdf/2609.29011",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bbkfdps8qv5z6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2609.29011",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29011"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Torelli Theorem for moduli stacks of vector bundles on tame Deligne Mumford curves",
  "title_text": "Torelli Theorem for moduli stacks of vector bundles on tame Deligne Mumford curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/bbkfdps8qv5z6",
  "venue": "arXiv",
  "versions": []
}