{
  "abstract": "We study the closed and open Gromov--Witten potentials of the toric Calabi--Yau threefold $$ X_p=\\operatorname{Tot}\\bigl(\\mathcal{O}_{\\mathbb{P}^{1}}(p-1)\\oplus\\mathcal{O}_{\\mathbb{P}^{1}}(-p-1)\\bigr),\\qquad p\\geq 2. $$ We prove closed and open mirror symmetry under a nonvanishing condition on the torus weights, relating these potentials to topological recursion on the mirror curves. We establish polynomial structures for both the higher-genus closed potentials and the stable open potentials. We also establish double-scaling limits for topological recursion on the mirror curves. In particular, our results for the closed potentials prove the higher-genus ansatz and the double-scaling conjecture of Caporaso--Griguolo--Mariño--Pasquetti--Seminara.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40257",
  "author_total": 3,
  "authors": [
    {
      "name": "Shuai Guo"
    },
    {
      "name": "Jingyi Xu"
    },
    {
      "name": "Qingsheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4s5a7j91d56ys.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40257",
  "fulltext_url": null,
  "id": "4s5a7j91d56ys",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40257",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7215132652",
  "pdf_url": "https://arxiv.org/pdf/2609.40257",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4s5a7j91d56ys.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40257",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40257"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Structure of higher-genus open-closed Gromov--Witten theory of $\\mathcal{O}_{\\mathbb{P}^{1}}(p-1)\\oplus\\mathcal{O}_{\\mathbb{P}^{1}}(-p-1)$",
  "title_text": "Structure of higher-genus open-closed Gromov--Witten theory of 𝒪_ℙ^1(p−1)⊕𝒪_ℙ^1(−p−1)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/4s5a7j91d56ys",
  "venue": "arXiv",
  "versions": []
}