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Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated
Multi angle
Authors : Botero, Ana (Author of the conference)
CIRM (Publisher )
11F50 - Jacobi forms
14C20 - Divisors, linear systems, invertible sheaves
14J15 - Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
32U05 - plurisubharmonic functions and generalizations
CIRM (Publisher )
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Abstract :
We show that the ring of Siegel-Jacobi forms of 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. This is joint work with José Burgos Gil, David Holmes and Robin de Jong.
Keywords : Mixed Shimura varieties; automorphic forms; Chern Weil theory; b-divisors; singular psh metrics
MSC Codes : Keywords : Mixed Shimura varieties; automorphic forms; Chern Weil theory; b-divisors; singular psh metrics
11F50 - Jacobi forms
14C20 - Divisors, linear systems, invertible sheaves
14J15 - Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
32U05 - plurisubharmonic functions and generalizations
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 17/11/2023 Conference Date : 11/10/2023 Subseries : Research talks arXiv category : Algebraic Geometry ; Number Theory Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:59:28 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-11_Botero.mp4 
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Information on the Event
Event Title : Global invariants of arithmetic varieties / Invariants globaux des variétés arithmétiquesEvent Organizers : Botero, Ana ; Freixas Montplet, Gérard ; Navarro Garmendia, Alberto ; Sombra, Martin Dates : 09/10/2023 - 13/10/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2857.html
Citation Data
DOI : 10.24350/CIRM.V.20102003Cite this video as: Botero, Ana (2023). Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20102003 URI : http://dx.doi.org/10.24350/CIRM.V.20102003 |
See Also
- [Multi angle] Eisenstein K3 surfaces, equivariant analytic torsion, and automorphic forms on complex balls / Author of the conference Yoshikawa, Ken-Ichi.
- [Multi angle] Torsion points of elliptic curves via Berkovich spaces over $\mathbb{Z}$ / Author of the conference Poineau, Jérôme.
- [Multi angle] José Burgos' variations of arithmetic intersection theory / Author of the conference Kramer, Jürg.
- [Multi angle] On harmonic weak Maass forms associated to even integer weight newforms / Author of the conference Alfes-Neumann, Claudia.
Bibliography
- BOTERO, Ana María, GIL, José Ignacio Burgos, HOLMES, David, et al. Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated. arXiv preprint arXiv:2203.14583, 2022. - https://arxiv.org/abs/2203.14583
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