Neron models of Green-Griffiths-Kerr and log Neron models

TL;DR

This paper establishes a homeomorphism between two different constructions of Néron models for variations of Hodge structures, connecting the classical and logarithmic approaches.

Contribution

It constructs a homeomorphism linking the Green-Griffiths-Kerr Néron model with the log Néron model by Kato, Nakayama, and Usui.

Findings

Established a topological equivalence between the two models.

Unified the classical and logarithmic perspectives on Néron models.

Enhanced understanding of the structure of admissible normal functions.

Abstract

For a variation of Hodge structure over a punctured disk, Green, Griffiths and Kerr introduced a N\'eron model which is a Hausdorff space that includes values of admissible normal functions. On the other hand, Kato, Nakayama and Usui introduced a N\'eron model as a logarithmic manifold using log mixed Hodge theory. This work constructs a homeomorphism between these two models.