Complex analytic Néron models for arbitrary families of intermediate Jacobians

Abstract

Given a family of intermediate Jacobians (for a polarizable variation of integral Hodge structure of odd weight) on a Zariski-open subset of a complex manifold, we construct an analytic space that naturally extends the family. Its two main properties are: (a) the horizontal and holomorphic sections are precisely the admissible normal functions without singularities; (b) the graph of any admissible normal function has an analytic closure inside our space. As a consequence, we obtain a new proof for the zero locus conjecture of M. Green and P. Griffiths. The construction uses filtered $\mathcal {D}$ -modules and M. Saito’s theory of mixed Hodge modules; it is functorial, and does not require normal crossing or unipotent monodromy assumptions.