Non-polyhedral effective cones from the moduli space of curves

Abstract

We show that the pseudoeffective cone of divisors ${\overline{\text{Eff}}}^1({\overline{\mathcal{M}}}_{g,n})$ for $g\ge 2$ and $n\ge 2$ is not polyhedral by showing that the class of the fibre of the morphism forgetting one point forms an extremal ray of the dual nef cone of curves ${\overline{\text{Nef}}}_1({\overline{\mathcal{M}}}_{g,n})$ and the cone at this ray is not polyhedral.

17 pages, 4 figures