Non-polyhedral effective cones from the moduli space of curves

Mullane, Scott

doi:10.1090/tran/8365

Non-polyhedral effective cones from the moduli space of curves
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Trans. Amer. Math. Soc. 374 (2021), 6397-6415 Request permission

Abstract:

We show that the pseudoeffective cone of divisors $\overline {\text {Eff}}^1(\overline {\mathcal {M}}_{{g}, {n}})$ for $g\geq 2$ and $n\geq 2$ 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.

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