1-Motives Associated to the Limiting Mixed Hodge Structures of Degenerations of Curves

TL;DR

This paper constructs Deligne 1-motives linked to the limiting mixed Hodge structures of semi-stable curve degenerations, using logarithmic structures and Steenbrink's complexes.

Contribution

It provides an explicit description of Deligne 1-motives associated with limiting mixed Hodge structures in the context of curve degenerations.

Findings

Deligne 1-motives are explicitly described for semi-stable degenerations.

Uses logarithmic structures and Steenbrink's complexes to analyze degenerations.

Connects mixed Hodge structures with algebraic 1-motives.

Abstract

In this article, we will give the Deligne 1-motives up to isogeny corresponding to the $\mathbb{Q}$-limiting mixed Hodge structures of semi-stable degenerations of curves, by using logarithmic structures and Steenbrink's cohomological mixed Hodge complexes associated to semi-stable degenerations of curves.