On an Equivalence of Divisors on $\overline {\text {M}}_{0,n}$ from Gromov-Witten Theory and Conformal Blocks

Abstract

AbstractWe consider a conjecture that identifies two types of base point free divisors on $\overline {\text {M}}_{0,n}$ M ¯ 0 , n . The first arises from Gromov-Witten theory of a Grassmannian. The second comes from first Chern classes of vector bundles associated with simple Lie algebras in type A. Here we reduce this conjecture on $\overline {\text {M}}_{0,n}$ M ¯ 0 , n to the same statement for n = 4. A reinterpretation leads to a proof of the conjecture on $\overline {\text {M}}_{0,n}$ M ¯ 0 , n for a large class, and we give sufficient conditions for the non-vanishing of these divisors.