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 the results of [\textit{J. I. Burgos Gil} et al., Lond. Math. Soc. Lect. Note Ser. 427, 45--77 (2016; Zbl 1378.14027)] to higher degrees.

14C17, 14E99, 32U05, 32U25, 52A39

singular metrics, non-pluripolar products, Chern-Weil theory, b-divisors

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Faculty of Mathematics, University of Regensburg, Germany

ICMAT (Instituto de Ciencias Matemáticas), Madrid, Spain

Mathematical Institute, University of Leiden, The Netherlands

Mathematical Institute, University of Leiden, The Netherlands