{
  "abstract": "In this paper we use the topological vertex formalism to derive a structural formula for the leading terms of the generating series of Gromov--Witten invariants of local $\\mathbb P^2$. Then we give two applications of this formula. First we use this result to derive an explicit formula for the leading terms of the transformed Gopakumar--Vafa invariants of local $\\mathbb P^2$. This is an extension of a formula of Guo--Zhou \\cite{gz} from degree $2d-5$ to $3d-1$, and shares some similar features with the famous Göttsche--Yau--Zaslow formula. And as the second application, we prove Guo--Wu--Moreira's Conjecture \\cite{gw} about the leading Betti numbers of the moduli space of one-dimensional Gieseker semistable sheaves on $\\mathbb P^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04483",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhiyuan Wang"
    },
    {
      "name": "Chenglang Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cge1qs4xfja88.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04483",
  "fulltext_url": null,
  "id": "cge1qs4xfja88",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04483",
  "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"
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    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SG"
    ],
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      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W7220745862",
  "pdf_url": "https://arxiv.org/pdf/2610.04483",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cge1qs4xfja88.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.04483",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04483"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "On leading Gopakumar--Vafa invariants of local $\\mathbb{P}^2$ and leading Betti numbers of moduli spaces of one-dimensional sheaves on $\\mathbb{P}^2$",
  "title_text": "On leading Gopakumar--Vafa invariants of local ℙ^2 and leading Betti numbers of moduli spaces of one-dimensional sheaves on ℙ^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/cge1qs4xfja88",
  "venue": "arXiv",
  "versions": []
}