Classifying spaces of degenerating mixed Hodge structures, III: Spaces of nilpotent orbits

TL;DR

This paper develops toroidal partial compactifications of moduli spaces of mixed Hodge structures, representing them as spaces of nilpotent orbits, advancing the understanding of degenerating mixed Hodge structures.

Contribution

It introduces new toroidal compactifications of moduli spaces of mixed Hodge structures as spaces of nilpotent orbits, extending previous theories.

Findings

Constructed toroidal partial compactifications of moduli spaces.

Represented these spaces as moduli of log mixed Hodge structures.

Provided a framework for studying degenerations of mixed Hodge structures.

Abstract

We construct toroidal partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients. They are moduli spaces of log mixed Hodge structures with polarized graded quotients. We construct them as the spaces of nilpotent orbits.