Geodesic
Chern-Weil and Hilbert-Samuel formulae for singular Hermitian line bundles
Documenta mathematica, Tome 27 (2022), pp. 2563-2623.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14C17, 14E99, 32U05, 32U25, 52A39
Keywords: singular metrics, non-pluripolar products, Chern-Weil theory, b-divisors 
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     author = {Botero, Ana Mar{\'\i}a and Burgos Gil, Jos\'e Ignacio and Holmes, David and de Jong, Robin},
     title = {Chern-Weil and {Hilbert-Samuel} formulae for singular {Hermitian} line bundles},
     journal = {Documenta mathematica},
     pages = {2563--2623},
     publisher = {mathdoc},
     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a3/}
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Botero, Ana María; Burgos Gil, José Ignacio; Holmes, David; de Jong, Robin. Chern-Weil and Hilbert-Samuel formulae for singular Hermitian line bundles. Documenta mathematica, Tome 27 (2022), pp. 2563-2623. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a3/