## Journal of Differential Geometry

### $\rm{SL}_2$-orbits and degenerations of mixed Hodge structure

Gregory Pearlstein

#### Abstract

We extend Schmid’s $\rm{SL}_2$-orbit theorem to a class of variations of mixed Hodge structure which normal functions, logarithmic deformations, degenerations of 1-motives and archimedean heights. In particular, as a consequence of 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.

#### Article information

Source
J. Differential Geom., Volume 74, Number 1 (2006), 1-67.

Dates
First available in Project Euclid: 30 March 2007

https://projecteuclid.org/euclid.jdg/1175266181

Digital Object Identifier
doi:10.4310/jdg/1175266181

Mathematical Reviews number (MathSciNet)
MR2260287

Zentralblatt MATH identifier
1107.14010

Subjects
Primary: 32Gxx: Deformations of analytic structures
Secondary: 14Dxx: Families, fibrations

#### Citation

Pearlstein, Gregory. $\rm{SL}_2$-orbits and degenerations of mixed Hodge structure. J. Differential Geom. 74 (2006), no. 1, 1--67. doi:10.4310/jdg/1175266181. https://projecteuclid.org/euclid.jdg/1175266181