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Quantitative arithmetic of diagonal degree $2$ K3 surfaces (1910.06257v2)
Published 14 Oct 2019 in math.NT and math.AG
Abstract: In this paper we study the existence of rational points for the family of K3 surfaces over $\mathbb{Q}$ given by $$w2 = A_1x_16 + A_2x_26 + A_3x_36.$$ 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.