  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.

Algebraic Geometry