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

By Ana Botero

Appears in collection : Global invariants of arithmetic varieties / Invariants globaux des variétés arithmétiques

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.

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Citation data

  • DOI 10.24350/CIRM.V.20102003
  • Cite this video Botero Ana (10/11/23). Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20102003
  • URL https://dx.doi.org/10.24350/CIRM.V.20102003

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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