{
  "abstract": "Let $X$ and $Y$ be smooth complex Fano manifolds of dimension at least three with very ample anticanonical bundles, and let $\\mathcal{E}_X$ and $\\mathcal{E}_Y$ be exceptional coherent sheaves on $X$ and $Y$, respectively. We prove that a Fourier--Mukai equivalence $\\mathcal{E}_X^\\perp\\simeq \\mathcal{E}_Y^\\perp$ implies $X\\simeq Y$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21904",
  "author_total": 1,
  "authors": [
    {
      "name": "Songtao Kenneth Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72tzwbywp8j0t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21904",
  "fulltext_url": null,
  "id": "72tzwbywp8j0t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21904",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222455398",
  "pdf_url": "https://arxiv.org/pdf/2610.21904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72tzwbywp8j0t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.21904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Reconstruction of Fano manifolds from the orthogonal to an exceptional coherent sheaf",
  "title_text": "Reconstruction of Fano manifolds from the orthogonal to an exceptional coherent sheaf",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/72tzwbywp8j0t",
  "venue": "arXiv",
  "versions": []
}