Contractible Extremal Rays on M_0,n

1996/07/07 by Keel, Sean, McKernan, James
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9607009

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 NE₁(M_n), and for the cone of divisors NE¹(Q_n). This second cone turns out to be simplicial. We give complete descriptions of NE₁(M_n) and NE₁(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.

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