Scaling of conformal blocks and generalized theta functions over \(\overline{\mathcal {M}}_{g,n}\). (English) Zbl 1388.14079
Summary: By way of intersection theory on \(\overline{\mathcal {M}}_{g,n}\), 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.
MSC:
| 14H10 | Families, moduli of curves (algebraic) |
| 14H42 | Theta functions and curves; Schottky problem |
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