摘要翻译：
设V是有限生成域K上的平面光滑三次曲线。V的Mordell-Weil定理表明，存在一个有限子集P\子集V(k)，使得整个V(k)可以由P通过先前构造的点对画割线和切线，并将它们的新交点与V连续相加而得到。本文给出了关于三次曲面类似陈述的数值数据。对于所考察的曲面，我们还检验了关于Fano簇上有界高有理点的渐近性与曲面Picard群秩的Manin猜想。
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英文标题：
《Mordell-Weil Problem for Cubic Surfaces, Numerical Evidence》
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作者：
Bogdan G. Vioreanu
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  Let V be a plane smooth cubic curve over a finitely generated field k. The Mordell-Weil theorem for V states that there is a finite subset P \subset V(k) such that the whole V(k) can be obtained from P by drawing secants and tangents through pairs of previously constructed points and consecutively adding their new intersection points with V. In this paper we present numerical data regarding the analogous statement for cubic surfaces. For the surfaces examined, we also test Manin's conjecture relating the asymptotics of rational points of bounded height on a Fano variety with the rank of the Picard group of the surface.
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PDF链接：
https://arxiv.org/pdf/0802.0742