I'll discuss a result that the Chow quotient parametrizing
configurations of n points in P^{d} which generically
lie on a rational normal curve is isomorphic to
M_{0,n}, generalizing the well-known d = 1 result of
Kapranov. The corresponding GIT quotients, for symmetric
linearization, are related to certain line bundles coming from
the genus zero WZW model in conformal field theory. A
representation-theoretic symmetry is manifest as the classical
Gale transform in this setting.