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

Abstract

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