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The Mori cones of moduli spaces of pointed curves of small genus

Gavril Farkas·Angela Gibney
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Abstract

We compute the Mori cone of curves of the moduli space \M_{g,n} of stable n-pointed curves of genus g in the case when g and n are relatively small. For instance, we show that for g<14 every curve in \M_g is numerically equivalent to an effective sum of 1-strata (loci of curves with 3g-4 nodes). We also prove that the nef cone of \M_{0,6} is composed of 11 natural subcones all contained in the convex hull of boundary classes. We apply this result to classify the fibrations of the moduli space of rational curves with n<7 marked points.

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Gavril Farkas, Angela Gibney. 2001-11-28. The Mori cones of moduli spaces of pointed curves of small genus. https://arxiv.org/abs/math/0111268

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