Extended period domains, algebraic groups, and higher Albanese manifolds

TL;DR

This paper constructs extended period domains for linear algebraic groups, interprets higher Albanese manifolds using these domains, and extends them through toroidal compactifications, advancing the understanding of mixed Hodge structures.

Contribution

It introduces extended period domains as toroidal compactifications for G-mixed Hodge structures and relates them to higher Albanese manifolds, providing a new geometric framework.

Findings

Construction of extended period domains as toroidal compactifications

Interpretation of higher Albanese manifolds via these domains

Extension of Albanese manifolds through compactifications

Abstract

For a linear algebraic group G over the field of rational numbers, we consider the period domains D classifying G-mixed Hodge structures, and construct the extended period domains as toroidal partial compactifications. We give an interpretation of higher Albanese manifolds by Hain and Zucker by using the above D for some G, and extend them via the toroidal partial compactifications.