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

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.

arXiv commentThe main result is stated in the introduction. The Q-steenbrink double complex is modified and simplified, and the final proof is simplified and cleaned. Also, One remark is added at the end