In the moduli space (or classification space) of complex algebraic curves there is so called {\it real locus}, which corresponds to the curves that can be defined over the reals. It leads, in a natural way, to a certain simplicial complex called the {\it real nerve} and the aim of our study is to find its geometrical and homological dimension. Though generally we deal with this question by the methods of hyperbolic geometry, using so called Fuchsian and non-euclidean crystallographic groups, at the last, decisive, stage one actually has to solve a certain combinatorial problem of setting, in a specific order, some amount of weighted points on a circle. The aim of the talk is to get the audience acquainted with this combinatorial face of our geometrically-homological problem, hoping it will get recognized by someone as a more general and known, from the combinatorial point of view. This is a joint work with Grzegorz Gromadzki.