Mathematische Zeitschrift

, Volume 284, Issue 3–4, pp 961–987 | Cite as

Scaling of conformal blocks and generalized theta functions over \(\overline{\mathcal {M}}_{g,n}\)

  • Prakash Belkale
  • Angela Gibney
  • Anna Kazanova


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.



P.B. was supported on NSF Grant DMS-0901249, and A.G. on DMS-1201268 and in part by DMS-1344994 (RTG in Algebra, Algebraic Geometry, and Number Theory, at UGA). We thank the anonymous referee for their time and thoughtful feedback.


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA
  2. 2.Department of MathematicsUniversity of GeorgiaAthensUSA

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