Special cycles on toroidal compactifications of orthogonal Shimura varieties

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 tor...

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Bibliographic Details
Published in:Mathematische annalen 2022-10, Vol.384 (1-2), p.1-63
Main Authors: Bruinier, Jan Hendrik, Zemel, Shaul
Format: Article
Language:English
Subjects:
Green's functions
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-021-02271-x