SL₂-orbits and degenerations of mixed Hodge structure

2003/09/26 by Gregory Pearlstein, Pearlstein, Gregory · 1 citation
Mathematics · #14C30 #14D07 #14G40 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C30 #msc:14D07 #msc:14G40

paper · pdf · doi:10.48550/arxiv.math/0309439

57 pages, amstex

arxiv created 2003/09/26 · arxiv updated 2009/12/01

Abstract

We prove an analog of Schmid's \rm SL₂-orbit theorem for a class of variations of mixed Hodge structure which includes logarithmic deformations, degenerations of 1-motives and archimedean heights. In particular, as consequence this theorem, we obtain a simple formula for the asymptotic behavior of the archimedean height of a flat family of algebraic cycles which depends only on the weight filtration and local monodromy.

Cited by

• Logarithmic geometry and Frobenius, II

Related

• Logarithmic geometry and Frobenius, II
• Degenerating complex variations of Hodge structure in dimension one
• Degenerations of Mixed Hodge structure
• Classifying spaces of degenerating mixed Hodge structures, VI: Log real analytic functions and log C^∞ functions
• 1-Motives Associated to the Limiting Mixed Hodge Structures of Degenerations of Curves