
Modul: MAT770 Oberseminar: Algebraische Geometrie
The singularities of the invariant metric of the sheaf of Jacobi forms on the universal elliptic curve
Prof. Dr. José Burgos Gill's talk Date: 27.04.15 Time: 13.15  14.45 Room: Y27H25 A theorem by Mumford implies that every automorphic line bundle on a pure
open Shimura variety, provided with an invariant smooth metric, can be
uniquely extended as a line bundle on a toroidal compactification of the
variety. In this extension, the metric acquires only logarithmic
singularities.
This result is the key to being able to compute arithmetic intersection
numbers from these line bundles. Hence it is natural to ask whether
Mumford's result remains valid for line bundles on mixed Shimura varieties.
In this talk we will examine the simplest case, namely the sheaf of Jacobi
forms on the universal elliptic curve. We will show that Mumford's result
can not be extended to this case and that a new interesting kind of
singularities appear.

