Density of rational points on diagonal bidegree $(1,2)$ hypersurface in ${\mathbb{P}}^{s-1}\times {\mathbb{P}}^{s-1}$

In this paper we establish an asymptotic formula for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface \begin{align*} x_1y_1^2+…+x_sy_s^2 = 0 \end{align*} in ${\mathbb{P}}^{s-1}\times {\mathbb{P}}^{s-1}$ with $s\ge 7$. This confirms the Manin conjecture for this variety.