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Complex analytic Néron models for arbitrary families of intermediate Jacobians

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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.

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Authors and Affiliations

  1. Department of Mathematics, Statistics & Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL, 60607, USA

    Christian Schnell

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  1. Christian Schnell
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Correspondence to Christian Schnell.

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Dedicated to Herb Clemens on the occasion of his 70th birthday

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Schnell, C. Complex analytic Néron models for arbitrary families of intermediate Jacobians. Invent. math. 188, 1–81 (2012). https://doi.org/10.1007/s00222-011-0341-8

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  • DOI: https://doi.org/10.1007/s00222-011-0341-8

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