Effective cones of quotients of moduli spaces of stable n-pointed curves of genus zero
William F. Rulla
Abstract
Let Xn := M0,n, the moduli space of n-pointed stable genus zero curves, and let Xn,m be the quotient of Xn by the action of the symmetric group Sn-m on the last n-m marked points. The cones of effective divisors of Xn,m, m = 0,1,2, are calculated. Using this, upper bounds for the cones Mov(Xn,m) generated by divisors with moving linear systems are calculated, m = 0,1, along with the induced bounds on the cones of ample divisors of Mg and Mg,1. As an application, the cone of effective divisors of M2,1 is analyzed in detail.
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