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arXiv · 2609.37420

Some applications of the moduli space of $U\oplus D_8(-1)$-polarized K3 surfaces

Adrian Clingher·Andreas Malmendier·Brandon Williams
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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 $k=1, 2$.

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Adrian Clingher, Andreas Malmendier, Brandon Williams. 2026-09-29. Some applications of the moduli space of $U\oplus D_8(-1)$-polarized K3 surfaces. https://arxiv.org/abs/2609.37420

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