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arXiv · 2112.09007

Chern-Weil and Hilbert-Samuel formulae for singular hermitian line bundles

Ana María Botero·José Ignacio Burgos Gil·David Holmes·Robin de Jong
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Abstract

We show a Chern-Weil type statement and a Hilbert-Samuel formula for a large class of singular plurisubharmonic metrics on a line bundle over a smooth projective complex variety. For this we use the theory of b-divisors and the so-called multiplier ideal volume function. We apply our results to the line bundle of Siegel-Jacobi forms over the universal abelian variety endowed with its canonical invariant metric. This generalizes a result of the second author for the universal family of elliptic curves to higher degrees.

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Ana María Botero, José Ignacio Burgos Gil, David Holmes, Robin de Jong. 2021-12-16. Chern-Weil and Hilbert-Samuel formulae for singular hermitian line bundles. https://arxiv.org/abs/2112.09007

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