On the generalized toroidal completion of period mappings

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.

arXiv comment4th Version: The main finiteness theorem fixed