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