CONFORMAL BLOCKS AND RATIONAL NORMAL CURVES

We prove that the Chow quotient parameterizing configurations of n points in P-d which generically lie on a rational normal curve is isomorphic to (M) over bar (0,n), generalizing the well-known d = 1 result of Kapranov. In particular, (M) over bar (0,n) admits birational morphisms to all the corresponding geometric invariant theory (GIT) quotients. For symmetric linearizations, the polarization on each GIT quotient pulls back to a divisor that spans the same extremal ray in the symmetric nef cone of (M) over bar (0,n) as a conformal blocks line bundle. A symmetry in conformal blocks implies a duality of point-configurations that comes from Gale duality and generalizes a result of Goppa in algebraic coding theory. In a suitable sense, (M) over bar (0,2m) is fixed pointwise by the Gale transform when d = m - 1 so stable curves correspond to self-associated configurations.