Boundary Components of Mumford-Tate Domains

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.

58 pages, 22 figures; final version, to appear in Duke Math. J.; section 6 substantially expanded

References in corpus (4)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint
• An Exponential History of Functions with Logarithmic Growth
• Semi-algebraic horizontal subvarieties of Calabi-Yau type

Cited by in corpus (12)

• Hodge theory of the middle convolution
• Polarized relations on horizontal SL(2)s
• Classification of horizontal SL(2)'s
• Extremal degenerations of polarized Hodge structures
• Asymptotics of degenerations of mixed Hodge structures
• Jumps in the Archimedean Height
• Hodge Representations
• Height functions for motives, II
• On the boundary of moduli spaces of log Hodge structures, II: nontrivial torsors
• Eigenperiods and the moduli of points in the line
• Classifying spaces of degenerating mixed Hodge structures, V: Extended period domains and algebraic groups
• Boundaries of cycle spaces and degenerating Hodge structures