  We prove a result of Chern-Weil type for canonically metrized line bundles on
one-parameter families of smooth complex curves. Our result generalizes a
result due to J.I. Burgos Gil, J. Kramer and U. K\"uhn that deals with a line
bundle of Jacobi forms on the universal elliptic curve over the modular curve
with full level structure, equipped with the Petersson metric. Our main tool,
as in the work by Burgos Gil, Kramer and K\"uhn, is the notion of a b-divisor.
