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- Kobayashi–Hitchin_correspondence abstract "In differential geometry, the Kobayashi–Hitchin correspondence(or Donaldson-Uhlenbeck-Yau theorem) relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles. The correspondence is named after Shoshichi Kobayashi and Nigel Hitchin, who independently conjectured in the 1980s that the moduli spaces of stable vector bundles and Einstein–Hermitian vector bundles over a complex manifold were essentially the same. This was proved by Donaldson for algebraic surfaces and later for algebraic manifolds, by Uhlenbeck and Yau for Kähler manifolds, and by Li and Yau for complex manifolds.There is a folklore conjecture right after S.-T. Yau's proof of the Calabi conjecture that polystable bundles admit Hermitian Yang-Mills connection. This is partially due to the argument of Bogomolov and the success of Yau's work on constructing global geometric structures in Kahler geometry.The most difficult part were accomplished by Simon Donaldson for algebraic surfaces and Uhlenbeck-Yau for general case around 1982, announced in various seminars and appeared in print in 1985.Soon after that, there are some formal publication of the conjecture due to Kobayashi. The program to carry out this deep theorem inspired by the work of Yau and Bogomolov is also called Donaldson-Uhlenbeck-Yau correspondence or DUY theorem. The proof of Uhlenbeck-Yau was the key to prove the later works in this direction, including the famous works of Carlos Simpson on Higgs bundle. This later work is also called SUY theorem on Higgs bundle.".
- Kobayashi–Hitchin_correspondence wikiPageExternalLink books?id=gxy85Qj3aa4C.
- Kobayashi–Hitchin_correspondence wikiPageExternalLink cpa.3160390714.
- Kobayashi–Hitchin_correspondence wikiPageID "37856668".
- Kobayashi–Hitchin_correspondence wikiPageLength "3183".
- Kobayashi–Hitchin_correspondence wikiPageOutDegree "12".
- Kobayashi–Hitchin_correspondence wikiPageRevisionID "690641823".
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Algebraic_manifold.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Algebraic_surface.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Category:Vector_bundles.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Communications_on_Pure_and_Applied_Mathematics.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Complex_manifold.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Differential_geometry.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Einstein–Hermitian_vector_bundle.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Kähler_manifold.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Nigel_Hitchin.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Shoshichi_Kobayashi.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Simon_Donaldson.
- Kobayashi–Hitchin_correspondence wikiPageWikiLink Stable_vector_bundle.
- Kobayashi–Hitchin_correspondence wikiPageWikiLinkText "Kobayashi–Hitchin correspondence".
- Kobayashi–Hitchin_correspondence wikiPageUsesTemplate Template:Citation.
- Kobayashi–Hitchin_correspondence wikiPageUsesTemplate Template:Differential-geometry-stub.
- Kobayashi–Hitchin_correspondence wikiPageUsesTemplate Template:Reflist.
- Kobayashi–Hitchin_correspondence subject Category:Vector_bundles.
- Kobayashi–Hitchin_correspondence type Bundle.
- Kobayashi–Hitchin_correspondence comment "In differential geometry, the Kobayashi–Hitchin correspondence(or Donaldson-Uhlenbeck-Yau theorem) relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles. The correspondence is named after Shoshichi Kobayashi and Nigel Hitchin, who independently conjectured in the 1980s that the moduli spaces of stable vector bundles and Einstein–Hermitian vector bundles over a complex manifold were essentially the same.".
- Kobayashi–Hitchin_correspondence label "Kobayashi–Hitchin correspondence".
- Kobayashi–Hitchin_correspondence sameAs Q6424285.
- Kobayashi–Hitchin_correspondence sameAs 小林・ヒッチン対応.
- Kobayashi–Hitchin_correspondence sameAs m.0n_b4ws.
- Kobayashi–Hitchin_correspondence sameAs Q6424285.
- Kobayashi–Hitchin_correspondence wasDerivedFrom Kobayashi–Hitchin_correspondence?oldid=690641823.
- Kobayashi–Hitchin_correspondence isPrimaryTopicOf Kobayashi–Hitchin_correspondence.