Year: 2026
Type: preprint
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 $k=1, 2$.
Source: arXiv (Cornell University)
Institution: University of Missouri–St. Louis
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7214995072