On the boundary of moduli spaces of log Hodge structures, II: nontrivial torsors

TL;DR

This paper investigates the triviality of torsors over moduli spaces of pure Hodge structures across various period domains, extending previous results and identifying conditions for non-triviality.

Contribution

It generalizes earlier findings by determining torsor triviality for all period domains of pure Hodge structures and explores non-triviality on open sets related to cycle spaces.

Findings

Trivial torsors in Hermitian symmetric cases

Non-trivial torsors on certain open sets

Extension of previous non-triviality results

Abstract

This is a continuous work of our previous paper. In the previous work we showed a triviality of the torsors in the case where period domains are Hermitian symmetric and a non-triviality for one-example. In this paper we determine whether the torsors are trivial or not for any period domains for pure Hodge structures. We also show a generalization of a previous result which gives a non-triviality on some open sets connecting to cycle spaces.