Boundary Components of Mumford-Tate Domains

TL;DR

This paper investigates the structure of boundary components in Mumford-Tate domains by analyzing nilpotent orbits, computing associated Mumford-Tate groups, and applying findings to variations of Hodge structure.

Contribution

It provides a minimal algebraic description of spaces of nilpotent orbits in Hodge domains and computes Mumford-Tate groups for generic limit mixed Hodge structures.

Findings

Spaces of nilpotent orbits are presented as iteratively fibered algebraic-group orbits.

Mumford-Tate groups of generic limit mixed Hodge structures are explicitly computed.

Applications demonstrate the relevance to variations of Hodge structure.

Abstract

We study certain spaces of nilpotent orbits in Hodge domains, and treat a number of examples. More precisely, we compute the Mumford-Tate group of the limit mixed Hodge structure of a generic such orbit. The result is used to present these spaces as iteratively fibered algebraic-group orbits in a minimal way. We conclude with two applications to variations of Hodge structure.