Density of rational points on a quadric bundle in P 3 × P 3
Density of rational points on a quadric bundle in P 3 × P 3
复制标题
DOI：
10.1215/00127094-2020-0031
复制
发表时间：
2018-05
期刊：
影响因子：
--
通讯作者：
T. Browning;D. R. Heath-Brown
中科院分区：
文献类型：
--
作者：
T. Browning;D. R. Heath-Brown
建立了$\mathbb {P}^3$中双投射超曲面x1y1^2 +\dots+ x4y4^2 =0$的某个Zebriki稠密子集上有界反正则高有理点数的渐近公式.这证实了修改后的Manin猜想，其中删除一个薄的合理点集是允许的。
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.