On holomorphic conformal structures associated with lattice polarized K3 surfaces

Abstract

We discuss the connection between Picard-Fuchs equations for certain families of lattice polarized K3 surfaces and the construction of integrable holomorphic conformal structures on their period domains. We then compute an explicit example of a locally conformally flat holomorphic metric associated with generic Jacobian Kummer surfaces, which allows for a novel description of the local variation of complex structure.