We study lines on smooth cubic surfaces over the field of p-adic numbers, from a theoretical and computational point of view. Segre showed that the possible counts of such lines are 0, 1, 2, 3, 5, 7, 9, 15 or 27. We show that each of these counts is achieved. Probabilistic aspects are investigated by sampling both p-adic and real cubic surfaces from different distributions and estimating the probability of each count.We link this to recent results on probabilistic enumerative geometry. Some experimental results on the Galois groups attached to p-adic cubic surfaces are also discussed.

中文翻译：

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p 进数和实立方面上的线

我们从理论和计算的角度研究p进数域上光滑立方表面上的线。Segre 表明，此类线的可能计数为 0、1、2、3、5、7、9、15 或 27。我们表明，每个计数都已实现。通过对不同分布的p进和实立方表面进行采样并估计每个计数的概率来研究概率方面。我们将其与概率枚举几何的最新结果联系起来。还讨论了 附加到p-进立方表面的伽罗瓦群的一些实验结果。