Density of Rational Points on diagonal bidegree (1, 2) hypersurface in P^{{s-1} 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 align* x₁y₁²+ +xₛyₛ² = 0align*in P^s-1 P^s-1 with s 7. This confirms the Manin conjecture for this variety.