Effective cones of quotients of moduli spaces of stable n-pointed curves of genus zero

Details Effective cones of quotients of moduli spaces of stable n-pointed curves of genus zero Effective cones of quotients of moduli spaces of stable n-pointed curves of genus zero

2003-11-20

arxiv.org/abs/math/0311358v2

Mathematics

Algebraic Geometry

Cleaned up version to appear in Trans. Amer. Math. Soc., corrections throughout. 19 pages, 8 figures

Scientific paper

Let X_n := \bar M_{0,n}, the moduli space of n-pointed stable genus zero curves, and let X_{n,m} be the quotient of X_n by the action of the symmetric group S_{n-m} on the last n-m marked points. The cones of effective divisors of X_{n,m}, m = 0,1,2, are calculated. Using this, upper bounds for the cones Mov(X_{n,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 \bar M_g and \bar M_{g,1}. As an application, the cone of effective divisors of \bar M_{2,1} is analyzed in detail.

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