Effective cones of quotients of moduli spaces of stable n-pointed curves of genus zero
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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.