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Cup products and mixed Hodge structures

J. H. M. Steenbrink
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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 H^i(X \setminus D) \otimes H^j(X,D) \to H^{i+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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J. H. M. Steenbrink. 1999-02-23. Cup products and mixed Hodge structures. https://arxiv.org/abs/math/9902134

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