Poincare polynomial for the moduli space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$ and the number of points in $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$

Abstract

We obtain a combinatorial proof that the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$ satisfies the recurrent formula for Poincare polynomials of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$.