JournalsdmVol. 27pp. 2563–2623

Chern–Weil and Hilbert–Samuel formulae for singular Hermitian line bundles

  • Ana María Botero

    Faculty of Mathematics, University of Regensburg, Germany

  • José Ignacio Burgos Gil

    ICMAT (Instituto de Ciencias Matemáticas), Madrid, Spain

  • David Holmes

    Mathematical Institute, University of Leiden, The Netherlands

  • Robin de Jong

    Mathematical Institute, University of Leiden, The Netherlands
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Abstract

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.

Cite this article

Ana María Botero, José Ignacio Burgos Gil, David Holmes, Robin de Jong, Chern–Weil and Hilbert–Samuel formulae for singular Hermitian line bundles. Doc. Math. 27 (2022), pp. 2563–2623

DOI 10.4171/DM/X36