Sampei Usui

(2)-orbit theorem for degeneration of mixed Hodge structure

First published in the Journal of Algebraic Geometry in vol.17 (2008), published by University Press, Inc

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

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.

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

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.

Images of extended period maps

First published in the Journal of Algebraic Geometry in vol.15 (2006), published by University Press, Inc