Papers › Quantitative arithmetic of diagonal degree $2$ K3 surfaces
Quantitative arithmetic of diagonal degree $2$ K3 surfaces
Damián Gvirtz-Chen, Daniel Loughran, Masahiro Nakahara
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In this paper we study the existence of rational points for the family of K3 surfaces over ℚ given by w² = A₁x₁⁶ + A₂x₂⁶ + A₃x₃⁶. When the coefficients are ordered by height, we show that the Brauer group is almost always trivial, and find the exact order of magnitude of surfaces for which there is a Brauer-Manin obstruction to the Hasse principle. Our results show definitively that K3 surfaces can have a Brauer-Manin obstruction to the Hasse principle that is only explained by odd order torsion.
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