Chern-Weil and Hilbert-Samuel formulae for singular Hermitian line bundles (Q2695714)

Summary: 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.