Chern-Weil and Hilbert-Samuel formulae for singular Hermitian line bundles. (English) Zbl 1520.14010
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 [J. I. Burgos Gil et al., Lond. Math. Soc. Lect. Note Ser. 427, 45–77 (2016; Zbl 1378.14027)] to higher degrees.
MSC:
| 14C17 | Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry |
| 14E99 | Birational geometry |
| 32U05 | Plurisubharmonic functions and generalizations |
| 32U25 | Lelong numbers |
| 52A39 | Mixed volumes and related topics in convex geometry |
Citations:
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