{
  "abstract": "We study K3 surfaces polarized by the lattice $U\\oplus D_8(-1)$ through elliptic fibrations and orthogonal modular forms. Using an alternate genus-one fibration and its relative Jacobian, we construct an explicit map from Vinberg's coefficient space to the Hashimoto--Ueda family. We also explain the geometric meaning of certain character forms associated with these moduli spaces and extend the relative-Jacobian construction to the exceptional lattices $U\\oplus E_8(-1)\\oplus A_k(-1)$ with $k=1, 2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37420",
  "author_total": 3,
  "authors": [
    {
      "name": "Adrian Clingher"
    },
    {
      "name": "Andreas Malmendier"
    },
    {
      "name": "Brandon Williams"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9awnzgcmpas1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37420",
  "fulltext_url": null,
  "id": "e9awnzgcmpas1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37420",
  "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": "W7214995072",
  "pdf_url": "https://arxiv.org/pdf/2609.37420",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9awnzgcmpas1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37420",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37420"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Some applications of the moduli space of $U\\oplus D_8(-1)$-polarized K3 surfaces",
  "title_text": "Some applications of the moduli space of U⊕ D_8(−1)-polarized K3 surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/e9awnzgcmpas1",
  "venue": "arXiv",
  "versions": []
}