Abstract
We study the Buchi K3 surface proving that it belongs to the one dimensional family of Kummer surfaces associated to genus two curves with automorphism group \(D_4\). We compute its Picard lattice and show that the rational points of the surface are Zariski-dense. Moreover, we provide analogous results for the Kummer surface associated to any genus two curve whose automorphism group contains a non-hyperelliptic involution.
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