Boundary complexes of moduli spaces of curves in higher genus

Abstract

Given a collection of boundary divisors in the moduli space M ¯ 0 , n \overline {\mathcal {M}}_{0,n} of stable genus-zero n n -pointed curves, Giansiracusa proved that their intersection is nonempty if and only if all pairwise intersections are nonempty. We give a complete classification of the pairs ( g , n ) (g,n) for which the analogous statement holds in M ¯ g , n \overline {\mathcal {M}}_{g,n} .