Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated
Botero AM, Gil JIB, Holmes D, de Jong R (2024)
Duke Mathematical Journal 173(12): 2315-2396.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Botero, Ana MariaUniBi;
Gil, José Ignacio Burgos;
Holmes, David;
de Jong, Robin
Einrichtung
Abstract / Bemerkung
We show that the ring of Siegel–Jacobi forms of fixed degree and of fixed or bounded ratio between weight and index is not finitely generated. Our main tool is the theory of toroidal b-divisors and their relation to convex geometry. As a byproduct of our methods, we prove a conjecture of Kramer about the representation of all Siegel–Jacobi forms as sections of certain line bundles and we recover a formula due to Tai for the asymptotic dimension of the space of Siegel–Jacobi forms of given ratio between weight and index.
Stichworte
b-divisors;
mixed Shimura varieties;
Okounkov bodies;
psh metrics;
Siegel–Jacobi forms
Erscheinungsjahr
2024
Zeitschriftentitel
Duke Mathematical Journal
Band
173
Ausgabe
12
Seite(n)
2315-2396
Urheberrecht / Lizenzen
ISSN
0012-7094
eISSN
1547-7398
Page URI
https://pub.uni-bielefeld.de/record/2979492
Zitieren
Botero AM, Gil JIB, Holmes D, de Jong R. Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated. Duke Mathematical Journal . 2024;173(12):2315-2396.
Botero, A. M., Gil, J. I. B., Holmes, D., & de Jong, R. (2024). Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated. Duke Mathematical Journal , 173(12), 2315-2396. https://doi.org/10.1215/00127094-2023-0059
Botero, Ana Maria, Gil, José Ignacio Burgos, Holmes, David, and de Jong, Robin. 2024. “Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated”. Duke Mathematical Journal 173 (12): 2315-2396.
Botero, A. M., Gil, J. I. B., Holmes, D., and de Jong, R. (2024). Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated. Duke Mathematical Journal 173, 2315-2396.
Botero, A.M., et al., 2024. Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated. Duke Mathematical Journal , 173(12), p 2315-2396.
A.M. Botero, et al., “Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated”, Duke Mathematical Journal , vol. 173, 2024, pp. 2315-2396.
Botero, A.M., Gil, J.I.B., Holmes, D., de Jong, R.: Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated. Duke Mathematical Journal . 173, 2315-2396 (2024).
Botero, Ana Maria, Gil, José Ignacio Burgos, Holmes, David, and de Jong, Robin. “Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated”. Duke Mathematical Journal 173.12 (2024): 2315-2396.
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arXiv: 2203.14583
Preprint: 10.48550/arXiv.2203.14583
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