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 inMathematische annalen Vol. 384; no. 1-2; pp. 1 - 63
Main Authors Bruinier, Jan Hendrik, Zemel, Shaul
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2022
Springer Nature B.V
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