On the generalized toroidal completion of period mappings

TL;DR

This paper introduces a new geometric completion method for period maps over quasi-projective varieties, offering a Hodge-theoretic perspective and an alternative to existing compactification techniques.

Contribution

It constructs a generalized toroidal completion of period mappings, extending Mumford's compactification and providing a new approach aligned with Kato--Nakayama--Usui's framework.

Findings

Provides a rich geometric and Hodge-theoretic completion of period maps.

Establishes an analog of Mumford's toroidal compactification for Hodge varieties.

Offers an alternative construction to existing methods.

Abstract

Given a period map defined over a quasi-projective variety, we construct a completion with rich geometric and Hodge-theoretic meaning. This result may be regarded as an analog of Mumford's toroidal compactification for locally symmetric Hodge varieties as well as a realizable alternative of Kato--Nakayama--Usui's construction.