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. Hodge structures have been generalized for all complex varieties (even if they are singular and non-complete) in the form of mixed Hodge structures, defined by Pierre Deligne (1970). A variation of Hodge structure is a family of Hodge structures parameterized by a manifold, first studied by Phillip Griffiths (1968). All these concepts were further generalized to mixed Hodge modules over complex varieties by Morihiko Saito (1989).
mathematics, a Hodgestructure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives...
In algebraic geometry, a mixed Hodgestructure is an algebraic structure containing information about the cohomology of general algebraic varieties. It...
Vallance Douglas Hodge as a result of a work in between 1930 and 1940 to enrich the description of de Rham cohomology to include extra structure that is present...
In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential...
In mathematics, mixed Hodge modules are the culmination of Hodge theory, mixed Hodgestructures, intersection cohomology, and the decomposition theorem...
In algebraic geometry and differential geometry, the nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after Kevin Corlette and...
related Hodge-theoretic concepts. This idea has applications in the theory of moduli spaces, in deformation theory and Fontaine's p-adic Hodge theory,...
This is shown using the Kodaira–Spencer map. In Hodge theory, there are objects called real Hodgestructures which are the data of a real vector space H R...
using a variation of Hodgestructure on the moduli of algebraic K3 surfaces to show that all such K3 surfaces have the same Hodge numbers. A more low-brow...
named the Hodge Building in memory of Colonel William Walter Hodge, commander of the 93rd Engineer Regiment on the Alcan Highway. The Hodge Building was...
a major developer in particular of the theory of variation of Hodgestructure in Hodge theory and moduli theory, which forms part of transcendental algebraic...
Hodge conjecture, for some applications. The theory of mixed Hodgestructures, a powerful tool in algebraic geometry that generalizes classical Hodge...
of Hodgestructures and mirror symmetry, and has written several books on Hodge theory. In 2002, Voisin proved that the generalization of the Hodge conjecture...
family (V, ρ ⋅ h) is a holomorphic family of Hodgestructures; moreover, it forms a variation of Hodgestructure, and X is a finite disjoint union of hermitian...
matrices are a useful technique for computing the Jacobian of a curve Hodgestructure – these are generalizations of Jacobians Honda–Tate theorem – classifies...
manifold with a Hodge metric is occasionally called a Hodge manifold (named after W. V. D. Hodge), so Kodaira's results states that Hodge manifolds are...
perverse sheaves, and the theory of variation of Hodge structures and mixed Hodgestructures (introduced by Pierre Deligne) in algebraic geometry. This...
setting such as Hodge theory of Kähler manifolds inspire understanding of Hodgestructures for varieties and schemes as well as p-adic Hodge theory, deformation...
solution Stratification (mathematics) Intersection homology Mixed Hodgestructure Whitney umbrella Round function Victor Goryunov Arnold, V. I. (2000)...
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