The cone of type A, level one conformal blocks divisors

Abstract

We prove that the type A, level one, conformal blocks divisors on $\bar{M}_{0,n}$ span a finitely generated, full-dimensional subcone of the nef cone. Each such divisor induces a morphism from $\bar{M}_{0,n}$, and we identify its image as a GIT quotient parameterizing configurations of points supported on a flat limit of Veronese curves. We show how scaling GIT linearizations gives geometric meaning to certain identities among conformal blocks divisor classes. This also gives modular interpretations, in the form of GIT constructions, to the images of the hyperelliptic and cyclic trigonal loci in $\bar{M}_{g}$ under an extended Torelli map.