{
  "abstract": "In this paper, we give a complete description of the Hilbert schemes of rational curves up to degree $6$ on a prime Fano threefold $X$ of degree $22$. One of the key ingredients in the geometry of these Hilbert schemes is the geometry of bisecant conics associated with rational curves on $X$. As applications, we describe additional geometric features of these moduli spaces and derive Donaldson--Thomas (DT) type invariants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08176",
  "author_total": 2,
  "authors": [
    {
      "name": "Kiryong Chung"
    },
    {
      "name": "Dae-Won Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b64p572fhawsk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08176",
  "fulltext_url": null,
  "id": "b64p572fhawsk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08176",
  "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": "W7212064161",
  "pdf_url": "https://arxiv.org/pdf/2609.08176",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b64p572fhawsk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08176",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08176"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hilbert schemes of low-degree rational curves on a prime Fano threefold of degree $22$",
  "title_text": "Hilbert schemes of low-degree rational curves on a prime Fano threefold of degree $22$",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/b64p572fhawsk",
  "venue": "arXiv",
  "versions": []
}