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Hodge structure

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…

Applications, Mixed Hodge structures & Hodge structures

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Overview

Hodge structures

Mixed Hodge structures

Examples

Applications

Variation of Hodge structure

Hodge modules

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Hodge structure

Nodes75
Edges74
Triples187
Avg. degree1.97
Density0.026667
Components1

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Hodge structure

Top relations

related to References · 87
Hodge structure → Actes, Alexander, American Journal, American Mathematical Society, An, An Overview, Arthur Ogus, Astérisque No, BF02684654, BF02684692, BF02685881, Bourbaki Exp, Christian, Colloque, Congrès International, Construction, Deligne, EMS Press, EMS PressPatrikis, Encyclopedia
related to Examples · 30
Hodge structure → Algebraic Manifolds, Any, Deligne, E2-page, Ehresmann, For, Friedrich Hirzebruch, From, Griffiths, He, Hence, Hodge, If, Jacobian, K3, Kähler, Lefschetz, More, Notice, Period Integrals
has application · 12
Hodge structure → Alexander Grothendieck, Arithmetic, C/R, Frobenius, Galois, Hodge, Methods, Rham, Sergei Gelfand, Since, The, Yuri Manin
related to Example of curves · 12
Hodge structure → Finally, First, Further, Hodge, Mixed Hodge Theory, Naive Guide, The, Then, There, This, To, Wn/Wn
related to Mixed Hodge structure in cohomology (Deligne's theorem) · 10
Hodge structure → Both, Deligne, For, Hironaka, Hodge, In, Künneth, Rham, The, This
related to A-Hodge structure · 9
Hodge structure → B-structures, Hodge, Hodge A-structure, Hodge A-structures, In, Noetherian, The, Then, There
related to Hodge modules · 6
Hodge structure → For, Hodge, Saito, There, These, They
related to Survey articles · 6
Hodge structure → Arapura, Bibcode, Donu, Geometric Variations, Mixed Hodge Structures Associated, PDF
related to Variation of Hodge structure · 6
Hodge structure → Griffiths, Hodge, More, Omega, OX, The
related to Definition of mixed Hodge structure · 4
Hodge structure → Fp, Here, Hodge, Wi

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Important terminology

hodge displaystyle structure cohomology mixed complex structures mathbb group filtration deligne varieties algebraic weight de variety pure theory manifold definition

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hodge structureis afamily of Hodge structures parameterized by a manifold0.90text
Hodge structurehas applicationThe0.60section
Hodge structurehas applicationHodge0.60section
Hodge structurehas applicationAlexander Grothendieck0.60section
Hodge structurehas applicationArithmetic0.60section
Hodge structurehas applicationFrobenius0.60section
Hodge structurehas applicationSergei Gelfand0.60section
Hodge structurehas applicationYuri Manin0.60section
Hodge structurehas applicationMethods0.60section
Hodge structurehas applicationGalois0.60section
Hodge structurehas applicationC/R0.60section
Hodge structurehas applicationRham0.60section

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