## Abstract

Let ℙ denote the weighted projective space with weights (1, 1, 1, 3) over the rationals, with coordinates

χ:

The surface χ is a K3 surface over the function field ℚ(t). In this paper, we explicitly compute the geometric Picard lattice of χ, together with its Galois module structure, as well as derive more results on the arithmetic of χ and other elements of the family

*x*,*y*,*z*and*w*; let χ be the generic element of the family of surfaces in ℙ given byχ:

*w*^{2}=*x*^{6}+*y*^{6}+*z*^{6}+*tx*^{2}*y*^{2}*z*^{2}.The surface χ is a K3 surface over the function field ℚ(t). In this paper, we explicitly compute the geometric Picard lattice of χ, together with its Galois module structure, as well as derive more results on the arithmetic of χ and other elements of the family

*x*.Original language | English |
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Number of pages | 20 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Early online date | 27 Mar 2018 |

DOIs | |

Publication status | E-pub ahead of print - 27 Mar 2018 |