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Complex analytic Néron models for arbitrary families of intermediate Jacobians
journal contributionposted on 2012-08-15, 00:00 authored by Christian Schnell
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 D-modules and M. Saito’s theory of mixed Hodge modules; it is functorial, and does not require normal crossing or unipotent monodromy assumptions
Publisher StatementPost print version of article may differ from published version. The original publication is available at springerlink.com; DOI: 10.1007/s00222-011-0341-8.