{
  "abstract": "For a vector bundle $E$ on a smooth projective curve $C$, one defines the Quot scheme $Q_d(E,C)$ parametrizing subsheaves of $E$ having length $d$ torsion quotients. If $E_i$ is a vector bundle of rank $r\\geq 2$ on a smooth projective curve $C_i$ for $i=1,2$, isomorphisms between $\\mathbb{P}_{C_i}(E_i)$ preserving the projective bundle structures induce isomorphisms of $Q_d(E_i,C_i)$, called natural isomorphisms. We show that for $d\\geq 2$ all isomorphisms between $Q_d(E_i,C_i)$ are natural, except for a non-natural involution of $Q_2(\\mathcal{O}_C^{\\oplus r},C)$. This gives a complete description of the automorphism group of $Q_d(E,C)$, generalizing previous works of Biswas-Dhillon-Hurtubise and Gangopadhyay. This also shows that one can reconstruct the curve from the Quot scheme, a Torelli-type theorem. As a key step in our proof, we show that any isomorphism between symmetric powers of smooth projective curves preserving big diagonals is natural, which is interesting in its own right.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14283",
  "author_total": 3,
  "authors": [
    {
      "name": "Ashima Bansal"
    },
    {
      "name": "Supravat Sarkar"
    },
    {
      "name": "Shivam Vats"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b84vpzy22wv2m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14283",
  "fulltext_url": null,
  "id": "b84vpzy22wv2m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14283",
  "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": "W7213284501",
  "pdf_url": "https://arxiv.org/pdf/2609.14283",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b84vpzy22wv2m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14283",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14283"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Torelli theorems for Quot schemes of vector bundles on curves",
  "title_text": "Torelli theorems for Quot schemes of vector bundles on curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/b84vpzy22wv2m",
  "venue": "arXiv",
  "versions": []
}