Cup products and mixed Hodge structures
Abstract
Let X be a complete complex nonsingular algebraic variety and D a closed algebraic subset of X. We show that the cup product maps Hi(X D) Hj(X,D) Hi+j(X,D) are morphisms of mixed Hodge structures. As a corollary we obtain a new proof of a duality result of Fujiki. We also deal with the extraordinary cup product.
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