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Chern-Weil theory and Hilbert-Samuel theorem for semi-positive singular toroidal metrics on line bundles
May 13, 2022 at 16:30 – 17:30 CEST
TGiZ-Seminar: Tropical geometry in Zoom (First meeting Summer Semester 2022)
José Ignacio Burgos Gil (ICMAT, Madrid)
In this talk I will report on joint work with A. Botero, D. Holmes and R. de Jong. Using the theory of b-divisors and non-pluripolar products we show that Chen-Weil theory and a Hilbert Samuel theorem can be extended to a wide class of singular semi-positive metrics. We apply the techniques relating semipositive metrics on line bundles to b-divisors to study the line bundle of Siegel-Jacobi forms with the Peterson metric. On the one hand we prove that the ring of Siegel-Jacobi forms of constant positive relative index is never finitely generated, and we recover a formula of Tai giving the asymptotic growth of the dimension of the spaces of Siegel-Jacobi modular forms.