Mixed Hodge structures
Fouad El Zein
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Source: Crossref
Published: Jan 1, 1983
DOI: 10.1090/s0002-9947-1983-0678337-5
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The theory of Mixed Hodge Structures (M.H.S.) on the cohomology of an algebraic variety X X over complex numbers was found by Deligne in 1970. The case when X X is a Normal Crossing Divisor is fundamental. When the variety X 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 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 Y .
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