Picard groups of Siegel modular 3-folds and \(\theta\)-liftings (Q2905191)
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scientific article; zbMATH DE number 6072207
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Picard groups of Siegel modular 3-folds and \(\theta\)-liftings |
scientific article; zbMATH DE number 6072207 |
Statements
24 August 2012
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Siegel modular threefold
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Picard group
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theta lifting
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math.AG
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math.RT
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Picard groups of Siegel modular 3-folds and \(\theta\)-liftings (English)
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The paper under review compares the Picard group (up to torsion) of coverings of the Siegel threefold. Firstly, by results of \textit{R. Weissauer} [J. Reine Angew. Math. 391, 100--156 (1988; Zbl 0657.10022)] this group is given by automorphic forms which are theta lifts. Secondly, these lifts correspond to certain special cycles, the Humbert surfaces. Thus the final result says that these span the Picard group \((\otimes Q)\).
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