Classification of horizontal SL(2)'s

Abstract

A variation of Hodge structure is a horizontal holomorphic mapping into a flag domain D; here "horizontal" indicates that the image of the map satisfies a system of partial differential equations known as the infinitesimal period relation (or Griffiths' transversality condition). Such maps arise as (lifts of) period mappings associated with families of polarized algebraic manifolds. The celebrated Nilpotent Orbit and SL(2)-Orbit Theorems of Schmid describe the asymptotic behavior of a variation of Hodge structure, and play a fundamental role in the analysis of singularities of the period mapping (equivalently, degenerations of Hodge structure). As a consequence, it became an important problem to describe the SL(2)'s appearing in Schmid's Theorem. We classify those horizontal SL(2)s and the related R-split polarized mixed Hodge structures. Many examples are included.

Final version (to appear in Compositio)

References in corpus (4)

• Extremal degenerations of polarized Hodge structures
• Asymptotics of degenerations of mixed Hodge structures
• Nilpotent cones and their representation theory
• Nilpotent cones and adjoint orbits

Cited by in corpus (9)

• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• Moduli Space Holography and the Finiteness of Flux Vacua
• Bulk Reconstruction in Moduli Space Holography
• Polarized relations on horizontal SL(2)s
• Nilpotent cones and their representation theory
• Hodge Representations
• Cycle connectivity and pseudoconcavity of flag domains
• Degenerations of Hodge structure
• Nilpotent cones and adjoint orbits