Abstract
We study a variant of the Néron models over curves which has recently been found by the second named author in a more general situation using the theory of Hodge modules. We show that its identity component is a certain open subset of an iterated blow-up along smooth centers of the Zucker extension of the family of intermediate Jacobians and that the total space is a complex Lie group over the base curve and is Hausdorff as a topological space. In the unipotent monodromy case, the image of the map to the Clemens extension coincides with the Néron model defined by Green, Griffiths and Kerr. In the case of families of Abelian varieties over curves, it coincides with the Clemens extension, and hence with the classical Néron model in the algebraic case (even in the non-unipotent monodromy case).
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Saito, M., Schnell, C. A variant of Néron models over curves. manuscripta math. 134, 359–375 (2011). https://doi.org/10.1007/s00229-010-0398-5
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DOI: https://doi.org/10.1007/s00229-010-0398-5