On a stratification of the Kontsevich moduli space M¯0,n(G(2,4),d) and enumerative geometry

We consider a particular stratification of the moduli space M¯0,n(G(2,4),d) of stable maps to G(2,4)G(2,4). As an application we compute the degree of the variety parametrizing rational ruled surfaces with a minimal directrix of degree d2−1 by studying divisors in this moduli space of stable maps. For example, there are 128054031872040 rational ruled sextics passing through 25 points in P3P3 with a minimal directrix of degree 2.