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

الأصل · EN

We compute the Mori cone of curves of the moduli space,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 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 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.