Chern-Weil and Hilbert-Samuel formulae for singular hermitian line bundles
Algebraic Geometry
2021-12-17 v1 Complex Variables
Differential Geometry
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 a result of the second author for the universal family of elliptic curves to higher degrees.
Keywords
Cite
@article{arxiv.2112.09007,
title = {Chern-Weil and Hilbert-Samuel formulae for singular hermitian line bundles},
author = {Ana María Botero and José Ignacio Burgos Gil and David Holmes and Robin de Jong},
journal= {arXiv preprint arXiv:2112.09007},
year = {2021}
}