  We study the Chow ring of the boundary of the partial compactification of the
universal family of principally polarized abelian varieties (ppav). We describe
the subring generated by divisor classes, and compute the class of the partial
compactification of the universal zero section, which turns out to lie in this
subring. Our formula extends the results for the zero section of the universal
uncompactified family.
  The partial compactification of the universal family of ppav can be thought
of as the first two boundary strata in any toroidal compactification of the
moduli space of ppav. Our formula provides a first step in a program to
understand the Chow groups of toroidal compactifications of the moduli of ppav,
especially of the perfect cone compactification, by induction on genus. By
restricting to the locus of Jacobians of curves, our results extend the results
of Hain on the double ramification (two-branch-point) cycle.
