2000/07/06 by Aroldo Kaplan, Kaplan, Aroldo, Gregory J. Pearlstein +2 · 1 citation
Mathematics · #14D07 #32G20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14D07 #msc:32G20
paper · pdf · doi:10.48550/arxiv.math/0007040
AMS-TeX, 29 pages. Additional results on unipotent variations
openalex publication_date 2000/07/06 · arxiv created 2002/03/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that a variation of graded-polarizable mixed Hodge structure over a punctured disk with unipotent monodromy, has a limiting mixed Hodge structure at the puncture (i.e., it is admissible in the sense of [SZ]) which splits over \R, if and only if certain grading of the complexified weight filtration, depending smoothly on the Hodge filtration, extends across the puncture. In particular, the result exactly supplements Schmid's Theorem for pure structures, which holds for the graded variation, and gives a Hodge-theoretic condition for the relative monodromy weight filtration to exist.