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

  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},
  pages={523 - 542}
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… 
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Being surfaces of intermediate type, i.e., neither geometrically rational or ruled, nor of general type, K3 surfaces have a rich yet accessible arithmetic theory, which has started to come into focus
PSP volume 166 issue 3 Cover and Back matter
  • Mathematical Proceedings of the Cambridge Philosophical Society
  • 2019


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