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 semi-stable reduction has been applied, we shall
  1. 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;
  2. define an Abel-Jacobi map for a normal crossing variety, and show that it gives the "limit" of the Abel-Jacobi mappings on the smooth fibres under the conditions of Zucker's theorem.
Two noteworthy consequences are: