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Transactions of the American Mathematical Society

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Mixed Hodge structures

Author: Fouad El Zein
Journal: Trans. Amer. Math. Soc. 275 (1983), 71-106
MSC: Primary 14C30; Secondary 14F40, 18E30, 32J25
MathSciNet review: 678337
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Abstract: The theory of Mixed Hodge Structures (M.H.S.) on the cohomology of an algebraic variety $X$ over complex numbers was found by Deligne in 1970. The case when $X$ is a Normal Crossing Divisor is fundamental. When the variety $X$ is embedded in a smooth ambient space we get the Mixed Hodge Structure using standard exact sequences in topology. This technique uses resolution of singularities one time for a complete variety and $2$ times for a quasi-projective one. As applications to the study of local cohomology we give the spectral sequence to the Mixed Hodge Structure on cohomology with support on a subspace $Y$.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1983 American Mathematical Society