Phillip Griffiths
Degeneration of Abel Jacobi mappings and Neron models for intermediate
jacobians
This is a report on joint work with Mark Green and Matt Kerr.
Given a family of polarized algebraic varieties over a one dimensional
base and to which semistable reduction has been applied, we
shall
 construct a Neron model,
which is a "slit" analytic fibre space of complex Lie groups, and
which graphs normal functions defined initially for the smooth fibres
in the family;
 define an AbelJacobi map for a normal
crossing variety, and show that it gives the "limit" of the
AbelJacobi mappings on the smooth fibres under the conditions
of Zucker's theorem.
Two noteworthy consequences are:

the limiting normal function associated to a family of
algebraic cycles necessarily involves the higher Chow groups and
regulator mappings;

there is a subtle constraint on the limiting AbelJacobi
mappings that is not present in the classical case of nodal
singularieties.