A variant of Neron models over curves

TL;DR

This paper investigates a new variant of Neron models over curves, utilizing Hodge modules, and establishes its geometric and topological properties, including its relation to classical Neron models and extensions.

Contribution

It introduces a novel variant of Neron models over curves, connecting them with Hodge modules, blow-ups, and classical models, expanding understanding of their structure and properties.

Findings

The identity component is an open subset of an iterated blow-up.

The total space forms a complex Lie group over the base curve.

In unipotent monodromy, it matches the Green-Griffiths-Kerr Neron model.

Abstract

We study a variant of the Neron models over curves which is recently 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 Neron 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 N\'eron model in the algebraic case (even in the non-unipotent monodromy case).