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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.