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Manuscripta Mathematica

, Volume 134, Issue 3–4, pp 359–375 | Cite as

A variant of Néron models over curves

  • Morihiko Saito
  • Christian SchnellEmail author
Article

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).

Mathematics Subject Classification (2000)

14D07 32G20 14K30 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.RIMS, Kyoto UniversityKyotoJapan
  2. 2.Department of Mathematics, Statistics and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA

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