In this paper, we compute the distributions of various markings on smooth cubic surfaces defined over the finite field \(\mathbb {F}_q\), for example the distribution of pairs of points, ‘tritangents’ or ‘double sixes’. We also compute the (rational) cohomology of certain associated bundles and covers over complex numbers.

中文翻译：

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三次曲面上的算术统计

在本文中，我们计算了在有限域\（\ mathbb {F} _q \）上定义的光滑三次曲面上的各种标记的分布，例如，点对，“三角”或“双六”的分布。我们还计算某些关联束的（理性）同调性，并覆盖复数。