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

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

2001-11-26

arxiv.org/abs/math/0111268v2

Transactions AMS 355 (2003), 1183-1199.

Mathematics

Algebraic Geometry

16 pages, references added

Scientific paper

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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