  We define an algebraic analogue, in the case of jacobians of curves, of the
height jump divisor introduced recently by R. Hain. We give explicit
combinatorial formulae for the height jump for families of semistable curves
using labelled reduction graphs. With these techniques we prove a conjecture of
Hain on the effectivity of the height jump, and also give a new proof of a
theorem of Tate, Silverman and Green on the variation of heights in families of
abelian varieties.
