Arithmetic statistics on cubic surfaces

Abstract

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.

Replaced to correct Theorem 2.3; 13 pages, 7 tables