Geodesic
Chern–Weil and Hilbert–Samuel formulae for singular Hermitian line bundles
Documenta mathematica, Tome 27 (2022), pp. 2563-2623 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/dm/x36
Classification : 14C17, 14E99, 32U05, 32U25, 52A39
Mots-clés : singular metrics, non-pluripolar products, Chern-Weil theory, b-divisors 
@article{10_4171_dm_x36,
     author = {Ana Mar{\'\i}a Botero and Jos\'e Ignacio Burgos Gil and Robin de Jong and David Holmes},
     title = {Chern{\textendash}Weil and {Hilbert{\textendash}Samuel} formulae for singular {Hermitian} line bundles},
     journal = {Documenta mathematica},
     pages = {2563--2623},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x36},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x36/}
}
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Ana María Botero; José Ignacio Burgos Gil; Robin de Jong; David Holmes. Chern–Weil and Hilbert–Samuel formulae for singular Hermitian line bundles. Documenta mathematica, Tome 27 (2022), pp. 2563-2623. doi: 10.4171/dm/x36

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