Complex-analytic Neron models for arbitrary families of intermediate Jacobians

Abstract

Given a family of intermediate Jacobians (for a polarized variation of Hodge structure of weight -1) 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 D-modules and M. Saito's theory of mixed Hodge modules; it is functorial, and does not require normal crossing or unipotent monodromy assumptions.

Fixed two small mistakes in section 24, as well as several typos

References in corpus (2)

• A generalization of the Neron models of Green, Griffiths and Kerr
• The zero locus of an admissible normal function

Cited by in corpus (4)

• A generalization of the Neron models of Green, Griffiths and Kerr
• The locus of Hodge classes in an admissible variation of mixed Hodge structure
• Analyticity of the closures of some Hodge theoretic subspaces
• A variant of Neron models over curves