On the boundary of the moduli spaces of log Hodge structures: triviality of the torsor

TL;DR

This paper investigates the structure of moduli spaces of log Hodge structures, focusing on the triviality of the torsor in cases involving Hermitian symmetric domains and mirror quintic type Hodge structures.

Contribution

It provides new insights into the triviality of the torsor within the moduli spaces of log Hodge structures for specific cases.

Findings

Triviality of the torsor in the Hermitian symmetric case

Triviality of the torsor for mirror quintic type Hodge structures

Enhanced understanding of the boundary behavior of moduli spaces

Abstract

In this paper we will study the moduli spaces of log Hodge structures introduced by Kato-Usui. This moduli space is a partial compactification of a discrete quotient of a period domain. We treat the following 2 cases: (A) the case where the period domain is Hermitian symmetric, (B) the case where the Hodge structures are of the mirror quintic type. Especially we study a property of the torsor.