{
  "abstract": "We construct and analyze a mirror family for the generalized complete intersection Calabi-Yau threefold $X_+=[\\mathbb{P}^1\\,|\\,3\\ {-1};\\ \\mathbb{P}^4\\,|\\,2\\ 3]$, with $(h^{1,1},h^{2,1})=(2,46)$. An auxiliary-variable presentation turns the negative-degree section into a variation of toric GIT. Crossing one wall flops 16 disjoint $(-1,-1)$-curves and yields a Calabi-Yau threefold $X_-$, a nef complete intersection in a toric $\\mathbb{Q}$-Fano eightfold, which carries a genus-one fibration of index 4. Because this ambient space is not Gorenstein, the Batyrev-Borisov construction does not apply. We use the Hori-Vafa equations only to select a 2-parameter Laurent family, and construct a smooth projective crepant compactification $Y$ of the Laurent model with $(h^{1,1},h^{2,1})=(46,2)$; for very general parameters the Mordell-Weil group is $\\mathbb{Z}/4\\mathbb{Z}$. The periods of $Y$ satisfy a rank-6 Picard-Fuchs system with two maximally unipotent boundary points, whose indicial algebras are isomorphic to the rational even cohomology rings of $X_-$ and $X_+$. The resulting genus-zero predictions agree with independent counts of 176 vertical lines and 100 vertical conics on the genus-one fibration $X_-\\to\\mathbb{P}^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03719",
  "author_total": 1,
  "authors": [
    {
      "name": "Atsushi Kanazawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/17kman30mq02z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03719",
  "fulltext_url": null,
  "id": "17kman30mq02z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03719",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220399432",
  "pdf_url": "https://arxiv.org/pdf/2610.03719",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/17kman30mq02z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03719",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03719"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Mirror symmetry for gCICY threefolds (I): a $[3,-1]$ block and a non-Gorenstein toric phase",
  "title_text": "Mirror symmetry for gCICY threefolds (I): a [3,−1] block and a non-Gorenstein toric phase",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/17kman30mq02z",
  "venue": "arXiv",
  "versions": []
}