Generalised automorphic sheaves and the proportionality principle of Hirzebruch-Mumford
Abstract: We axiomatise the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalised automorphic sheaf is proposed which includes sheaves of (meromorphic) sections of automorphic vector bundles with prescribed vanishing and pole orders along strata in the compactification, and their quotients. These include, for instance, sheaves of Jacobi forms and weakly holomorphic modular forms. Using this machinery, we give a short and purely algebraic proof of the proportionality theorem of Hirzebruch and Mumford
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Notes
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Journal of the Institute of Mathematics of Jussieu. - 23, 4 (2024) , 1567-1605, ISSN: 1475-3030
- DOI
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10.1017/s1474748023000300
- URN
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urn:nbn:de:bsz:25-freidok-2409889
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:37 AM CEST
Data provider
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Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Hörmann, Fritz
- Universität
Time of origin
- 2023
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