论文标题
四分之一的表面，其咬合和理性点
Quartic surface, its bitangents and rational points
论文作者
论文摘要
令X为平滑的四分之一表面，不包含在数字k上定义的线。我们证明，X对X定义有限的Bitangents有限。该结果可以解释为表明某个具有消失的不规则性的表面仅包含有限的许多理性点。在我们的证明中，我们使用与X相关的四分之一双实线的线的几何形状。在某些方向上，我们表明，在一个数字k上的任何四分之一的表面X上，x（\ overeline k）中的代数点集，它们在合适的k'k'k'k'k'k'k'k'上是二次的kariski densensense。
Let X be a smooth quartic surface not containing lines, defined over a number field K. We prove that there are only finitely many bitangents to X which are defined over K. This result can be interpreted as saying that a certain surface, having vanishing irregularity, contains only finitely many rational points. In our proof, we use the geometry of lines of the quartic double solid associated to X. In a somewhat opposite direction, we show that on any quartic surface X over a number field K, the set of algebraic points in X(\overeline K) which are quadratic over a suitable finite extension K' of K is Zariski-dense.
