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 $\overline{{\mathcal{M}}_{0,n}}(\mathbb{C})$.