Degenerating Hodge structure of one-parameter family of Calabi-Yau threefolds

TL;DR

This paper investigates the behavior of the extended period map at maximally unipotent monodromy points in one-parameter Calabi-Yau threefold families and proves a generic Torelli theorem for many such families.

Contribution

It introduces an analysis of the extended period map's image at special monodromy points and establishes a broad Torelli theorem for Calabi-Yau threefold families.

Findings

Characterization of the extended period map at maximally unipotent monodromy points

Proof of the generic Torelli theorem for a large class of Calabi-Yau threefolds

Advancement in understanding the log Hodge theory in this context

Abstract

To a one-parameter family of Calabi-Yau threefolds, we can associate the extended period map by the log Hodge theory of Kato and Usui. In the present paper, we study the image of a maximally unipotent monodromy point under the extended period map. As an application, we prove the generic Torelli theorem for a large class of one-parameter families of Calabi-Yau threefolds.