{
  "abstract": "In this paper we consider the $n-3$ dimensional linear section $X_Π$ of the Grassmannian $\\mathbb G(1,n)$ of lines in $\\mathbb P^n$ with a general linear space $Π$ of codimension $n+1$, with $n=2k+1$ odd and $n\\geq 5$, that is a Calabi-Yau variety. Related to $X_Π$ there is a degree $k+1$ Pfaffian hypersurface $\\mathcal C_Π$ that is the intersection of the dual of $\\mathbb G(1,n)$ with $Π^\\perp$. We prove that $\\mathcal C_Π$ is rational and we provide a birational parametrization of it. Moreover we study in some detail the congruence of lines of $\\mathbb P^n$ given by the centers of the linear complexes parametrised by the points of $\\mathcal C_Π$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11925",
  "author_total": 3,
  "authors": [
    {
      "name": "Michele Bolognesi"
    },
    {
      "name": "Ciro Ciliberto"
    },
    {
      "name": "Alessandro Verra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0w3zf3sfetd8z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11925",
  "fulltext_url": null,
  "id": "0w3zf3sfetd8z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11925",
  "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": "W7221151204",
  "pdf_url": "https://arxiv.org/pdf/2610.11925",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0w3zf3sfetd8z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11925",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11925"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On Calabi-Yau varieties that are linear sections of Grassmannians of lines",
  "title_text": "On Calabi-Yau varieties that are linear sections of Grassmannians of lines",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/0w3zf3sfetd8z",
  "venue": "arXiv",
  "versions": []
}