Classifying spaces of degenerating mixed Hodge structures, V: Extended period domains and algebraic groups

TL;DR

This paper develops extended period domains for classifying degenerating mixed Hodge structures, providing new compactifications and insights into the geometry of these moduli spaces.

Contribution

It introduces extended period domains and toroidal compactifications for mixed Hodge structures associated with algebraic groups, advancing the understanding of their degenerations.

Findings

Construction of extended period domains $D_{BS}$, $D_{SL(2)}$, and $ ext{Gamma} ackslash D_{ ext{Sigma}}$

Toroidal partial compactifications of mixed Mumford--Tate domains

Enhanced understanding of degenerations in mixed Hodge structures

Abstract

For a linear algebraic group $G$ over $\bf Q$, we consider the period domains $D$ classifying $G$-mixed Hodge structures, and construct the extended period domains $D_{\mathrm{BS}}$, $D_{\mathrm{SL}(2)}$, and $\Gamma \backslash D_{\Sigma}$. In particular, we give toroidal partial compactifications of mixed Mumford--Tate domains.