Complex-analytic Neron models for arbitrary families of intermediate Jacobians

Christian Schnell

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arXiv · 0910.0662

Complex-analytic Neron models for arbitrary families of intermediate Jacobians

Christian Schnell

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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.

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Christian Schnell. 2009-10-05. Complex-analytic Neron models for arbitrary families of intermediate Jacobians. https://arxiv.org/abs/0910.0662

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