Integral points and effective cones of moduli spaces of stable maps (Q1430447)

The authors compute the cone of effective \({\mathcal G}_n\)-invariant divisors of the Fulton-MacPherson configuration space of \(n\)-points of \(\mathbb{P}^1\) (over the simplex field). They use this result to provide a geometric interpretation of the \textit{W. Duke}, \textit{Z. Rudnick} and \textit{P. Sarnak} asymptotic formula for the number \(N_+(B)\) of binary forms, with integers coefficients, bounded by \(B\) which are \(\text{SL}_2(\mathbb{Z})\)-equivalent to a given form \(f\) of degree \(n\geq 3\) [Duke Math. J. 71, No. 1, 143--179 (1993; Zbl 0798.11024)].