Lowest Weights in Cohomology of Variations of Hodge Structure

2007/08/01 by Chris Peters, Peters, Chris · 1 citation
Mathematics · #14D07 #32G20 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:14D07 #msc:32G20

paper · pdf · doi:10.48550/arxiv.0708.0130

9 pages

arxiv created 2007/08/02 · arxiv updated 2009/12/01

Abstract

Let X be a smooth complex projective variety, let j:U\into X an immersion of a Zariski open subset, and let V be a variation of Hodge structure of weight n over U. Then IH^k(X, j_*V) is known to carry a pure Hodge structure of weight k+n, while H^k(U,V) carries a mixed Hodge structure of weight ≥ k+n. In this note it is shown that the image of the natural map IH^k(X,j_*V) → H^k(U,V) is the lowest weight part of this mixed Hodge structure. The proof uses Saito's theory of mixed Hodge modules.

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• Lowest Weights in Cohomology of Variations of Hodge Structure (II)

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