Chern-Weil theory and Hilbert-Samuel theorem for semi-positive singular toroidal metrics on line bundles

Jose Ignacio Burgos Gil (Instituto de Ciencias Matemáticas)

12-Apr-2022, 14:00-15:00 (24 months ago)

Abstract: 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.

algebraic geometry

Audience: researchers in the topic


ZAG (Zoom Algebraic Geometry) seminar

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Organizers: Jesus Martinez Garcia*, Ivan Cheltsov*, Jungkai Chen, Jérémy Blanc, Ernesto Lupercio, Yuji Odaka, Zsolt Patakfalvi, Julius Ross, Cristiano Spotti, Chenyang Xu
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