Rings of Siegel–Jacobi forms of bounded relative index are not finitely generated

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Sep 2024Embargo end date: 01 Jan 2022 Spain, Germany, Netherlands Publisher:Duke University PressJournal:Duke Mathematical Journal, volume 173 (issn: 0012-7094,

Copyright policy )Funded by:NWO | Moduli, metrics, models, ..., DFG | Higher Invariants – Inter...

Authors: Botero, A.M.; Burgos, G.J.I.; Holmes, D.S.T.; Jong, R.S. de;

doi: 10.1215/00127094-2023-0059 , 10.48550/arxiv.2203.14583

arXiv: 2203.14583

handle: 10261/381551 , 1887/4172822

Rings of Siegel–Jacobi forms of bounded relative index are not finitely generated

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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.

Countries

Spain, Germany, Netherlands

Related Organizations

Leiden University
Netherlands
Autonomous University of Madrid
Spain
Spanish National Research Council
Spain
Bielefeld University
Germany
Institute of Mathematical Sciences
Spain

Keywords

mixed Shimura varieties, Mathematics - Number Theory, 14C20, 11F50, 32U05, 14J15, Okounkov bodies, Psh metrics, Moduli, classification: analytic theory; relations with modular forms, Siegel-Jacobi forms, Mixed Shimura varieties, 510, Modular and Shimura varieties, Mathematics - Algebraic Geometry, Siegel–Jacobi forms, psh metrics, b-divisors, Jacobi forms, FOS: Mathematics, Divisors, linear systems, invertible sheaves, Number Theory (math.NT), Plurisubharmonic functions and generalizations, Algebraic Geometry (math.AG)

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