• DOI:10.1017/S0305004118000087
• Corpus ID: 119580402

On the arithmetic of a family of degree - two K3 surfaces

@article{Bouyer2018OnTA,
  title={On the arithmetic of a family of degree - two K3 surfaces},
  author={Florian Bouyer and Edgar Costa and Dino Festi and C. Nicholls and Mckenzie West},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2018},
  volume={166},
  pages={523 - 542}
}

• F. Bouyer, Edgar Costa, +2 authors Mckenzie West
• Published 6 March 2017
• Mathematics
• 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.