1 September 2024 Rings of Siegel–Jacobi forms of bounded relative index are not finitely generated
Ana María Botero, José Ignacio Burgos Gil, David Holmes, Robin de Jong
Author Affiliations +
Duke Math. J. 173(12): 2315-2396 (1 September 2024). DOI: 10.1215/00127094-2023-0059

Abstract

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.

Citation

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Ana María Botero. José Ignacio Burgos Gil. David Holmes. Robin de Jong. "Rings of Siegel–Jacobi forms of bounded relative index are not finitely generated." Duke Math. J. 173 (12) 2315 - 2396, 1 September 2024. https://doi.org/10.1215/00127094-2023-0059

Information

Received: 7 November 2022; Revised: 1 September 2023; Published: 1 September 2024
First available in Project Euclid: 26 September 2024

zbMATH: 07928012
MathSciNet: MR4801594
Digital Object Identifier: 10.1215/00127094-2023-0059

Subjects:
Primary: 11F50 , 14C20 , 14J15 , 32U05

Keywords: b-divisors , mixed Shimura varieties , Okounkov bodies , psh metrics , Siegel–Jacobi forms

Rights: Copyright © 2024 Duke University Press

Vol.173 • No. 12 • 1 September 2024
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