Scaling of conformal blocks and generalized theta functions over M¯ _{g , n}

By way of intersection theory on 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.