On an Equivalence of Divisors on M ¯ 0 , n from Gromov-Witten Theory and Conformal Blocks.

Abstract

We consider a conjecture that identifies two types of base point free divisors on ${\overline{M}}_{0,n}$ . 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 ${\overline{M}}_{0,n}$ to the same statement for n = 4. A reinterpretation leads to a proof of the conjecture on ${\overline{M}}_{0,n}$ for a large class, and we give sufficient conditions for the non-vanishing of these divisors.