Contractible Extremal Rays on \overline{M}_{0,n}

Abstract

We consider the cones of curves and divisors on the moduli space of stable pointed rational curves,M_n, and on the quotient by the symmetric group, Q_n, which is a moduli space of pairs. We find generators for contractible extremal rays of the cone of curves NE_1(M_n), and for the cone of divisors NE^1(Q_n). This second cone turns out to be simplicial. We give complete descriptions of NE_1(M_n) and NE_1(Q_n) for small n (< 8 in the first case, < 11 in the second). We also have results of independent interest on when curves in a divisor generate the cone of curves of the ambient variety.

16 pages,AMSTex

Cited by in corpus (13)

• ${\overline{M}}_{0,n}$ is not a Mori Dream Space
• Numerical criteria for divisors on $\M_{g}$ to be ample
• Effective divisors on moduli spaces of curves and abelian varieties
• $s{l}_2$ conformal block divisors and the nef cone of ${\bar{M}}_{0,n}$
• Conformal blocks divisors on ${\bar{M}}_{0,n}$ from $s{l}_2$
• Positivity of divisors on blown-up projective spaces, II
• A simplicial approach to effective divisors in ${\overline{M}}_{0,n}$
• GIT and moduli with a twist
• An outline of the log minimal model program for the moduli space of curves
• $s{l}_n$ level 1 conformal blocks divisors on ${\bar{M}}_{0,n}$
• Moduli spaces of weighted stable curves and log canonical models of ${\bar{M}}_{g,n}$
• Towards Fulton's conjecture
• Positive divisors on quotients of ${\bar{M}}_{0,n}$ and the Mori cone of ${\bar{M}}_{g,n}$