Abstract
Let be an irreducible complex analytic space with an immersion of a smooth Zariski-open subset, and let be a variation of Hodge structure of weight over . Assume that is compact Kähler. Then, provided that the local monodromy operators at infinity are quasi-unipotent, is known to carry a pure Hodge structure of weight , while carries a mixed Hodge structure of weight at least . In this note it is shown that the image of the natural map 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 is not a hypersurface.
Citation
Chris Peters. Morihiko Saito. "Lowest weights in cohomology of variations of Hodge structure." Nagoya Math. J. 206 1 - 24, June 2012. https://doi.org/10.1215/00277630-1548466
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