Scaling of conformal blocks and generalized theta functions over   $\bar{M}_{g,n}$
  By way of intersection theory on $\bar M_{g,n}$, we show that geometric interpretations for conformal blocks, as sections of ample line bundles over projective varieties, do not have to hold at points on the boundary. We show such a translation would imply certain recursion relations for first Chern classes of these bundles. While recursions can fail, geometric interpretations are shown to hold under certain conditions. 
Prakash Belkale, Angela Gibney, Anna Kazanova
math.AG