Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914746656096256 |
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| author | Botero, Ana María Gil, José Ignacio Burgos Holmes, David de Jong, Robin |
| author_facet | Botero, Ana María Gil, José Ignacio Burgos Holmes, David de Jong, Robin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_14583 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated Botero, Ana María Gil, José Ignacio Burgos Holmes, David de Jong, Robin Algebraic Geometry Number Theory 14C20, 11F50, 32U05, 14J15 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. |
| title | Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated |
| topic | Algebraic Geometry Number Theory 14C20, 11F50, 32U05, 14J15 |
| url | https://arxiv.org/abs/2203.14583 |