论文标题
$ p $ - adic和真实立方表面的线条
Lines on $p$-adic and real cubic surfaces
论文作者
论文摘要
从理论和计算的角度来看，我们在$ p $ adadig数字的领域的平滑立方体表面上研究线。塞格尔（Segre）表明，此类行的可能计数为$ 0,1,2,3,5,7,9,15 $或27美元。我们证明这些计数都是实现的。还通过从不同分布中对$ p $ - adiC和真实的立方表面进行抽样并估算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形状的最新结果联系起来。还讨论了有关$ p $ - 亚种立方体表面的GALOIS组的一些实验结果。
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 also 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.
