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 in . This confirms the modified Manin conjecture for this variety, in which the removal of a “thin” set of rational points is allowed.
"Density of rational points on a quadric bundle in ." Duke Math. J. 169 (16) 3099 - 3165, 1 November 2020. https://doi.org/10.1215/00127094-2020-0031