{
  "abstract": "We recover closed Gromov-Witten invariants and renormalized mirror periods for $K_{\\mathbb{P}^2}$ by the same operation on a wall function. This gives a direct passage from the Gross-Siebert construction of intrinsic mirror pairs to classical enumerative mirror symmetry. The link is a polynomiality theorem for punctured invariants. Assuming the expected identification with the normalized slab function, we also obtain a finite tree sum for closed Gromov-Witten invariants in terms of types of plane tropical curves. The mechanism is expected to extend to more general Calabi-Yau mirror pairs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04252",
  "author_total": 2,
  "authors": [
    {
      "name": "Michel van Garrel"
    },
    {
      "name": "Bernd Siebert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1r939rwnq1rbd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04252",
  "fulltext_url": null,
  "id": "1r939rwnq1rbd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04252",
  "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",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220692927",
  "pdf_url": "https://arxiv.org/pdf/2610.04252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1r939rwnq1rbd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04252"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "From wall structures to closed mirror symmetry. The case of $K_{\\mathbb{P}^2}$: Renormalized periods over the positive real locus, closed Gromov-Witten invariants from wall functions, and tropical enumeration",
  "title_text": "From wall structures to closed mirror symmetry. The case of K_ℙ^2: Renormalized periods over the positive real locus, closed Gromov-Witten invariants from wall functions, and tropical enumeration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1r939rwnq1rbd",
  "venue": "arXiv",
  "versions": []
}