{
  "abstract": "We study the polynomiality of combined logarithmic and ordinary Gromov-Witten invariants with a Lambda class insertion on toric surfaces $Δ(\\mathbf{c},\\mathbf{d})$. We show that the combined logarithmic Gromov-Witten invariants can be expressed in terms of universal relative node polynomials when the direction vector $\\mathbf{c}$ and length vector $\\mathbf{d}$ of the $h$-transverse lattice polygon $Δ(\\mathbf{c},\\mathbf{d})$ are sufficiently large and spread out. In particular, when the normal fan of the $h$-transverse lattice polygon $Δ(\\mathbf{c},\\mathbf{d})$ is smooth and its edges satisfy a length condition, we show that the combined Gromov-Witten invariants are equal to a universal node polynomial. We also show that the higher genus Block-Göttsche polynomials of smooth toric surfaces corresponding to these $h$-transverse lattice polygons, including toric blowups beyond Hirzebruch and toric del Pezzo surfaces, are equal to a generating function of higher genus Gromov-Witten invariants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35122",
  "author_total": 2,
  "authors": [
    {
      "name": "Yanqiao Ding"
    },
    {
      "name": "Dadi Ni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/325eyenh1vv4e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35122",
  "fulltext_url": null,
  "id": "325eyenh1vv4e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35122",
  "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": "W7223932473",
  "pdf_url": "https://arxiv.org/pdf/2610.35122",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/325eyenh1vv4e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35122",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35122"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Universal polynomials for Gromov-Witten invariants on toric surfaces",
  "title_text": "Universal polynomials for Gromov-Witten invariants on toric surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/325eyenh1vv4e",
  "venue": "arXiv",
  "versions": []
}