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

2001/11/28 by Gavril Farkas, Angela Gibney · 2 citations
Mathematics · #math.AG #msc:14H10

paper · pdf

published as Transactions AMS 355 (2003), 1183-1199. · 16 pages, references added

arxiv created 2001/11/28 · arxiv updated 2009/11/30

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.

Cited by

• Symmetric and non-symmetric F-conjectures are equivalent
• Remarks on two problems by Hassett

Related

• Towards the ample cone of \mgn
• Positive divisors on quotients of M_0,n and the Mori cone of M_g,n
• On the rationality of moduli spaces of pointed curves
• On the effective cone of the moduli space of pointed rational curves
• Small rational curves on the moduli space of stable bundles