2008/12/11 by Chris Peters, Peters, Chris, Morihiko Saito +1
Mathematics · #14C30 #32S35 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14C30 #msc:32S35
paper · pdf · doi:10.48550/arxiv.0812.2132
Extends results of preprint (arXiv:0708.0130v2) by the first author with the same title in the analytic context. Accepted for publication by Nagoya Math. Journal
arxiv created 2008/12/11 · openalex publication_date 2008/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be an irreducible complex analytic space with j:U\into X an immersion of a smooth Zariski open subset, and let \bV be a variation of Hodge structure of weight n over U. Assume X is compact Kähler. Then provided the local monodromy operators at infinity are quasi-unipotent, IHk(X, \bV) is known to carry a pure Hodge structure of weight k+n, while Hk(U,\bV) carries a mixed Hodge structure of weight ≥ k+n. In this note it is shown that the image of the natural map IHk(X,\bV) → Hk(U,\bV) is the lowest weight part of this mixed Hodge structure. In the algebraic case this easily follows from the formalism of mixed sheaves, but the analytic case is rather complicated, in particular when the complement X-U is not a hypersurface.