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Some applications of the moduli space of U⊕ D8(−1)-polarized K3 surfaces

  • Adrian Clingher
  • Andreas Malmendier
  • Brandon Williams
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Abstract

We study K3 surfaces polarized by the lattice U⊕ D8(−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⊕ E8(−1)⊕ Ak(−1) with k=1, 2.

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Cite

BibTeXRIS
BibTeX
@misc{clingher2026some,
  title = {{Some applications of the moduli space of $U\oplus D_8(-1)$-polarized K3 surfaces}},
  author = {Adrian Clingher and Andreas Malmendier and Brandon Williams},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37420},
  eprint = {2609.37420},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37420},
}
RIS
TY  - UNPB
TI  - Some applications of the moduli space of U⊕ D_8(−1)-polarized K3 surfaces
AU  - Adrian Clingher
AU  - Andreas Malmendier
AU  - Brandon Williams
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37420
UR  - https://arxiv.org/abs/2609.37420
AB  - We study K3 surfaces polarized by the lattice U⊕ 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⊕ E_8(−1)⊕ A_k(−1) with k=1, 2.
ER  -