SL_2-orbits and degenerations of mixed Hodge structure

Details SL_2-orbits and degenerations of mixed Hodge structure SL_2-orbits and degenerations of mixed Hodge structure

2003-09-26

arxiv.org/abs/math/0309439v1

Mathematics

Algebraic Geometry

57 pages, amstex

Scientific paper

We prove an analog of Schmid's $\text{\rm SL}_2$-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.

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