About: Mixed Hodge structure

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In algebraic geometry, a mixed Hodge structure is an algebraic structure containing information about the cohomology of general algebraic varieties. It is a generalization of a Hodge structure, which is used to study smooth projective varieties. In mixed Hodge theory, where the decomposition of a cohomology group may have subspaces of different weights, i.e. as a direct sum of Hodge structures

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  • In algebraic geometry, a mixed Hodge structure is an algebraic structure containing information about the cohomology of general algebraic varieties. It is a generalization of a Hodge structure, which is used to study smooth projective varieties. In mixed Hodge theory, where the decomposition of a cohomology group may have subspaces of different weights, i.e. as a direct sum of Hodge structures where each of the Hodge structures have weight . One of the early hints that such structures should exist comes from the long exact sequence of a pair of smooth projective varieties . The cohomology groups (for ) should have differing weights coming from both and . (en)
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  • In algebraic geometry, a mixed Hodge structure is an algebraic structure containing information about the cohomology of general algebraic varieties. It is a generalization of a Hodge structure, which is used to study smooth projective varieties. In mixed Hodge theory, where the decomposition of a cohomology group may have subspaces of different weights, i.e. as a direct sum of Hodge structures (en)
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  • Mixed Hodge structure (en)
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