2009/10/05 by Christian Schnell, Schnell, Christian
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.0910.0662
Fixed two small mistakes in section 24, as well as several typos
openalex publication_date 2009/10/05 · arxiv created 2010/07/20 · arxiv updated 2010/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.