Abstract

Each projective smooth algebraic variety over the complex numbers has a pure Hodge structure on its cohomology from the theory of compact Kaehler manifolds. Deligne has introduced the notion of a mixed Hodge structure and in three steps shown that: (1) a proper smooth variety has pure Hodge structure, (2) an open variety has a mixed Hodge structure, and (3) a singular variety has a mixed Hodge structure. We will define a mixed Hodge structure and survey Deligne's constructions followed by examples of mixed Hodge structures.

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