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K3 SURFACES AND ORTHOGONAL MODULAR FORMS
Part of:
Forms and linear algebraic groups
Surfaces and higher-dimensional varieties
Discontinuous groups and automorphic forms
Published online by Cambridge University Press: 29 August 2025
Abstract
We determine explicit generators for the ring of modular forms associated with the moduli spaces of K3 surfaces with automorphism group 
$(\mathbb {Z}/2\mathbb {Z})^2$ and of Picard rank 13 and higher. The K3 surfaces in question carry a canonical Jacobian elliptic fibration and the modular form generators appear as coefficients in the Weierstrass-type equations describing these fibrations.
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