Special cycles on toroidal compactifications of orthogonal Shimura varieties

Jan Hendrik Bruinier; Shaul Zemel

doi:https://doi.org/10.1007/s00208-021-02271-x

Special cycles on toroidal compactifications of orthogonal Shimura varieties

Jan Hendrik Bruinier, Shaul Zemel

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1-63
Number of pages	63
Journal	Mathematische Annalen
Volume	384
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-021-02271-x
State	Published - Oct 2022

All Science Journal Classification (ASJC) codes

Mathematics(all)

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https://doi.org/10.1007/s00208-021-02271-x

Cite this

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title = "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.",

author = "Bruinier, {Jan Hendrik} and Shaul Zemel",

note = "Funding Information: The first author is partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) TRR 326 Geometry and Arithmetic of Uniformized Structures, project number 444845124, and the LOEWE research unit USAG. Publisher Copyright: {\textcopyright} 2021, The Author(s).",

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Special cycles on toroidal compactifications of orthogonal Shimura varieties

Abstract

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