Given a simple Lie algebra g, a positive integer $\ell$ called the level, and an appropriately chosen n-tuple of dominant integral weights lambda of level $\ell$, one can define a vector bundle on the stacks M_{g,n} whose fibers are the so-called vector spaces of conformal blocks. On M_{0,n}, first Chern classes of these vector bundles turn out to be semi-ample divisors, and so define morphisms. In this talk I will discuss the simplest examples of these divisors, and show that they can be treated entirely combinatorially. I'll show that every morphism we know of on M_{0,n} comes from one of these divisors and even some that we didn't.

This is about joint work with Alexeev and Swinarski as well as some graduate students at UGA.