Room 70A, Ross Building, Jerusalem, Israel
A well-known result of Borcherds yields the modularity of Heegner divisors on complex orthogonal Shimura varieties (i.e. Grassmannian quotients). These varieties are typically non-compact, and one way of completing them to compact varieties is via toroidal compactifications. However, the boundary components there also contain divisors. We show how to extend the Heegner divisors to such compactifications in such a manner that the modularity result of Borcherds still holds. This is joint work with J. Bruinier.