Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

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.

Citations (9)

Summary

We haven't generated a summary for this paper yet.