In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives to the cohomology groups of a smooth and compact Kähler manifold. A mixed Hodge structure is a generalization, defined by Pierre Deligne (1970), that applies to all complex varieties (even if they are singular and non-complete). A variation of Hodge structure is a family of Hodge structures parameterized by a manifold, first studied by P. A. Griffiths (1968). All these concepts were further generalized to mixed Hodge modules over complex varieties by M. Saito (1989).
Read more about Hodge Structure: Hodge Structures, Mixed Hodge Structures, Examples, Applications, Variation of Hodge Structure, Hodge Modules
Famous quotes containing the word structure:
“I really do inhabit a system in which words are capable of shaking the entire structure of government, where words can prove mightier than ten military divisions.”
—Václav Havel (b. 1936)