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

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arxiv 2203.14583 v2 pith:ACRN45EW submitted 2022-03-28 math.AG math.NT

Ana María Botero , José Ignacio Burgos Gil , David Holmes , Robin de Jong This is my paper · ORCID
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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.

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  1. Analytic Bertini theorem II --- The local case

    math.AG 2026-07 accept novelty 8.0 of 10

    The local analytic Bertini theorem holds: multiplier ideal sheaves of psh functions on polydisc products restrict to fibers outside a pluripolar set.

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