Classifying spaces of degenerating mixed Hodge structures, II: Spaces of SL(2)-orbits

TL;DR

This paper introduces an enlarged classifying space for mixed Hodge structures by incorporating SL(2)-orbits, providing a real analytic and log-structured space that clarifies the SL(2)-orbit theorem in multiple variables.

Contribution

It constructs a new space integrating mixed Hodge theoretic SL(2)-orbits, enhancing understanding of degenerations in mixed Hodge structures.

Findings

Enlarged classifying space with real analytic and log structures

Natural interpretation of the SL(2)-orbit theorem in multiple variables

Framework for studying degenerations of mixed Hodge structures

Abstract

We construct an enlargement of the classifying space of mixed Hodge structures with polarized graded quotients, by adding mixed Hodge theoretic version of SL(2)-orbits. This space has a real analytic structure and a log structure with sign. The SL(2)-orbit theorem in several variables for mixed Hodge structures can be understood naturally with this space.