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  1. ; ; ; ; (, Mathematical Proceedings of the Cambridge Philosophical Society)
    Abstract Let ℙ denote the weighted projective space with weights (1, 1, 1, 3) over the rationals, with coordinates x , y , z and w ; let $$\mathcal{X}$$ be the generic element of the family of surfaces in ℙ given by \begin{equation*}X\colon w^2=x^6+y^6+z^6+tx^2y^2z^2.\end{equation*} The surface $$\mathcal{X}$$ is a K3 surface over the function field ℚ( t ). In this paper, we explicitly compute the geometric Picard lattice of $$\mathcal{X}$$ , together with its Galois module structure, as well as derive more results on the arithmetic of $$\mathcal{X}$$ and other elements of the family X . 
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