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arXiv · 1805.10715

Density of rational points on a quadric bundle in $\mathbb{P}^3\times \mathbb{P}^3$

T. D. Browning·D. R. Heath-Brown
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Abstract

An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface $x_1y_1^2+\dots+x_4y_4^2=0$ in $\mathbb{P}^3\times\mathbb{P}^3$. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed.

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T. D. Browning, D. R. Heath-Brown. 2018-05-27. Density of rational points on a quadric bundle in $\mathbb{P}^3\times \mathbb{P}^3$. https://doi.org/10.1215/00127094-2020-0031

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