Chern-Weil and Hilbert-Samuel formulae for singular hermitian line bundles

2021/12/16 by Botero, Ana María, Gil, José Ignacio Burgos, Holmes, David +1 · 2 citations
#14C17 #14E99 #32U05 #32U25 #52A39 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.09007

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.

Cited by

• Degeneration of the archimedean height pairing of algebraically trivial cycles
• Positive cones of b-divisor classes

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