{
  "abstract": "Using K-moduli spaces for log quasimaps $q_t\\colon\\left(\\mathbb P^1,\\frac{1-t}{12}D\\right)\\to[\\mathbb A^2/\\mathbb G_m]$ of degree twelve with twelve points and weight $t/12$, we construct a modular interpolation $\\{\\mathcal M_t\\}_{0\\le t\\le1}$ between the Baily--Borel compactification of the Heckman--Looijenga ball quotient $X_o$ and Miranda's GIT compactification of the moduli space of rational elliptic surfaces. We completely determine the wall-crossing and, for every rational $t\\in[0,1]$, identify \\[ \\mathcal M_t\\cong\\operatorname{Proj}R\\!\\left(X_o,\\mathcal L+\\frac t2Δ(6)+\\frac t3Δ(9)\\right), \\] where $\\mathcal L$ is the automorphic $\\mathbb Q$-line bundle and $Δ(6),Δ(9)$ are distinguished Heegner divisors. On the automorphic side, we construct a new automorphic form on $X_o$ via a Borcherds product, whose divisor gives an independent relation among the Heegner divisors. This relation provides a key input for determining the birational transformations in the K-moduli wall-crossing. As part of this analysis, we show that the first positive chamber $\\mathcal M_t$ for $t\\in (0,1/7)$ is Looijenga's semi-toroidal compactification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10777",
  "author_total": 2,
  "authors": [
    {
      "name": "Masafumi Hattori"
    },
    {
      "name": "Yota Maeda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/at0m96pb8we3c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10777",
  "fulltext_url": null,
  "id": "at0m96pb8we3c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10777",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221161687",
  "pdf_url": "https://arxiv.org/pdf/2610.10777",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/at0m96pb8we3c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10777",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10777"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "K-Moduli Wall Crossing and Automorphic Forms for the Moduli Space of Rational Elliptic Surfaces",
  "title_text": "K-Moduli Wall Crossing and Automorphic Forms for the Moduli Space of Rational Elliptic Surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/at0m96pb8we3c",
  "venue": "arXiv",
  "versions": []
}