Special Cycles on Toroidal Compactifications of Orthogonal Shimura Varieties

Abstract

We determine the behavior of automorphic Green functions along the boundary components of toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define boundary components of special divisors and prove that the generating series of the resulting special divisors on a toroidal compactification is modular.

arXiv comment57 pages, Example 3.28 added, some proofs in Section 4 expanded