Integral points and effective cones of moduli spaces of stable maps

Abstract

Consider the Fulton-MacPherson configuration space of n points on ℙ¹, which is isomorphic to a certain moduli space of stable maps to ℙ¹. We compute the cone of effective $\mathfrak{S}$_n-invariant divisors on this space. This yields a geometric interpretation of known asymptotic formulas for the number of integral points of bounded height on compactifications of SL₂ in the space of binary forms of degree n≥3