论文标题
单独的弗雷尼斯不足
Freeness alone is insufficient for Manin-Peyre
论文作者
论文摘要
Manin的猜想预测了Fano品种上有界高度的合理点的数量。为了确切的预测，有必要删除一个薄薄的有理点的子集。 Peyre暂时提出的是用他定义的特定freeness函数的点集取代该子集的集合。我们表明，在$ \ operatorname {hilb}^2（\ mathbb p^n）$的情况下，该提案失败了，因为通常的薄子集由抬高到某个双重盖的有理点组成，包含许多点，其中许多点具有相对较大的freeness。
Manin's conjecture predicts the number of rational points of bounded height on a Fano variety. To make this prediction precise, it is necessary to remove a thin subset of rational points. Peyre has tentatively proposed replacing this subset by the set of points where a certain freeness function he defined takes small values. We show that this proposal fails in the case of $\operatorname{Hilb}^2(\mathbb P^n)$, because the usual thin subset, consisting of rational points that lift to a certain double cover, contains many points with relatively large freeness.
