论文标题
Batyrev-tschinkel的猜想，用于非正常立方体表面及其对称方形
The Batyrev-Tschinkel conjecture for a non-normal cubic surface and its symmetric square
论文作者
论文摘要
我们通过对$ t_0^2 t_2 = t_1^2 t_3 $在任何数字字段上进行计数来完成对不可证实的非正常立方体表面上有界高度点的研究。我们表明，生长的顺序与Batyrev和Manin的猜想一致，并且该常数反映了Batyrev和Tschinkel的猜想所预测的品种的几何形状。然后，我们提供其对称方形$ \ mathrm {sym}^2 w $的点计数。尽管我们可以解释计数函数的主要术语，但是batyrev-manin猜想只有在删除薄套件后才能满足。最后，我们将计数的主要术语解释在$ \ mathrm {sym}^2（\ mathbb p^2 \ times \ times \ mathbb p^1）$由le Rudulier使用这些猜想所做的。
We complete the study of points of bounded height on irreducible non-normal cubic surfaces by doing the point count on the cubic surface $W$ given by $t_0^2 t_2 = t_1^2 t_3$ over any number field. We show that the order of growth agrees with a conjecture by Batyrev and Manin and that the constant reflects the geometry of the variety as predicted by a conjecture of Batyrev and Tschinkel. We then provide the point count for its symmetric square $\mathrm{Sym}^2 W$. Although we can explain the main term of the counting function, the Batyrev--Manin conjecture is only satisfied after removing a thin set. Finally we interpret the main term of the count on $\mathrm{Sym}^2(\mathbb P^2 \times \mathbb P^1)$ done by Le Rudulier using these conjecture.
