  We identify certain Gromov-Witten invariants counting rational curves with
given incidence and tangency conditions with the Betti numbers of moduli spaces
of point configurations in projective spaces. On the Gromov-Witten side, S.
Fomin and G. Mikhalkin established a recurrence relation via tropicalization,
which is realized on the moduli space side using Donaldson-Thomas invariants of
subspace quivers.
