  Kontsevich and Manin gave a formula for the number $N_e$ of rational plane
curves of degree $e$ through $3e-1$ points in general position in the plane.
When these $3e-1$ points have coordinates in the rational numbers, the
corresponding set of $N_e$ rational curves has a natural Galois-module
structure. We make some extremely preliminary investigations into this Galois
module structure, and relate this to the deck transformations of the generic
fibre of the product of the evaluation maps on the moduli space of maps. We
then study the asymptotics of the number of rational points on hypersurfaces of
low degree, and use this to generalise our results by replacing the projective
plane by such a hypersurface.
