Singularities of Variations of Mixed Hodge Structure
نویسندگان
چکیده
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, has a real limit at 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.
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