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Hodge variety

concept 1 articles 6 citations 8 shown relations

MathematicsAnalysisManifoldsKähler Metric

whose fundamental form defines an integral cohomology class. A compact complex manifold is a Hodge manifold if and only if it is isomorphic to a smooth algebraic subvariety of some complex projective space (Kodaira's projective imbedding theorem).

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Hodge manifold

A complex manifold on which a Hodge metric can be given, that is, a Kähler metric whose fundamental form defines an integral cohomology class. A compact complex manifold is a Hodge manifold if and only if it is isomorphic to a smooth algebraic subvariety of some complex projective space (Kodaira's projective imbedding theorem).

References

[1]	P.A. Griffiths, J.E. Harris, "Principles of algebraic geometry" , 1 , Wiley (1978) MR0507725 Zbl 0408.14001

How to Cite This Entry:
Hodge variety. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hodge_variety&oldid=23856

This article was adapted from an original article by A.L. Onishchik (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article

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Kähler MetricMathematics / Analysis / Manifolds / Kähler Metricmethod: title_similarity - confidence: 0.90suggested

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Hodge varietyencyclopedia_of_mathematics

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Complex manifoldoutgoing citation Kähler manifoldoutgoing citation Kähler metricoutgoing citation Manifoldincoming citation Intermediate Jacobianincoming citation Kähler manifoldincoming citation

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discussesarticle:eom--hodge-variety--3e41197514 -> concept:hodge-varietyconfidence: 1.00 - provenance: encyclopedia_of_mathematicsconfirmed

citesconcept:hodge-variety -> concept:complex-manifoldconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:hodge-variety -> concept:kahler-manifoldconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:hodge-variety -> concept:kahler-metricconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:manifold -> concept:hodge-varietyconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:intermediate-jacobian -> concept:hodge-varietyconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:kahler-manifold -> concept:hodge-varietyconfidence: 1.00 - provenance: article backlink extractionreviewed

subcategory_ofconcept:hodge-variety -> topic:k-hler-metricconfidence: 0.90 - provenance: title_similarity classificationsuggested

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