About: Birkhoff–Grothendieck theorem

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In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic vector bundle over is a direct sum of holomorphic line bundles. The theorem was proved by Alexander Grothendieck , and is more or less equivalent to Birkhoff factorization introduced by George David Birkhoff.

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rdfs:label	Birkhoff–Grothendieck theorem (en) Теорема Гротендика о расщеплении (ru) Теорема Гротендіка про розщеплення (uk) 伯克霍夫-格罗滕迪克定理 (zh)
rdfs:comment	In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic vector bundle over is a direct sum of holomorphic line bundles. The theorem was proved by Alexander Grothendieck , and is more or less equivalent to Birkhoff factorization introduced by George David Birkhoff. (en) Теорема Гротендика о расщеплении даёт классификацию голоморфных векторных расслоений над комплексной проективной прямой.А именно, она утверждает, что каждое голоморфное векторное расслоение над является прямой суммой голоморфных 1-мерных расслоений. (ru) Теорема Гротендіка про розщеплення дає класифікацію голоморфних векторних розшарувань над комплексною проективною прямою.А саме, вона стверджує, що кожне голоморфне векторне розшарування над є прямою сумою голоморфних 1-вимірних розшарувань. (uk) 在代数几何学中，伯克霍夫-格罗滕迪克定理（英文：Birkhoff–Grothendieck theorem）刻画了复射影直线上的全纯向量丛。具体而言，所有上的全纯向量丛都是全纯线丛的直和。 (zh)
dcterms:subject	Vector bundles Theorems in algebraic geometry Theorems in complex geometry Theorems in projective geometry
Wikipage page ID	14675761 (xsd:integer)
Wikipage revision ID	1100877720 (xsd:integer)
Link from a Wikipage to another Wikipage	Algebraic geometry of projective spaces Holomorphic vector bundle Mathematics Splitting principle Vector bundles Jumping line K-theory Line bundle Projective line Theorems in algebraic geometry Theorems in complex geometry Birkhoff factorization Theorems in projective geometry Vector bundle Euler sequence Algebraic vector bundle Serre twist Trivial bundle
sameAs	Birkhoff–Grothendieck theorem Birkhoff–Grothendieck theorem Birkhoff–Grothendieck theorem Birkhoff–Grothendieck theorem Birkhoff–Grothendieck theorem Birkhoff–Grothendieck theorem
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Reflist dbt:Short_description dbt:Harvs dbt:Algebraic_curves_navbox dbt:Topology-stub
authorlink	Alexander Grothendieck (en) George David Birkhoff (en)
first	Alexander (en) George David (en)
last	Grothendieck (en) Birkhoff (en)
year	1909 (xsd:integer) 1957 (xsd:integer)
loc	Theorem 2.1 (en)
has abstract	In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic vector bundle over is a direct sum of holomorphic line bundles. The theorem was proved by Alexander Grothendieck , and is more or less equivalent to Birkhoff factorization introduced by George David Birkhoff. (en) Теорема Гротендика о расщеплении даёт классификацию голоморфных векторных расслоений над комплексной проективной прямой.А именно, она утверждает, что каждое голоморфное векторное расслоение над является прямой суммой голоморфных 1-мерных расслоений. (ru) Теорема Гротендіка про розщеплення дає класифікацію голоморфних векторних розшарувань над комплексною проективною прямою.А саме, вона стверджує, що кожне голоморфне векторне розшарування над є прямою сумою голоморфних 1-вимірних розшарувань. (uk) 在代数几何学中，伯克霍夫-格罗滕迪克定理（英文：Birkhoff–Grothendieck theorem）刻画了复射影直线上的全纯向量丛。具体而言，所有上的全纯向量丛都是全纯线丛的直和。 (zh)
prov:wasDerivedFrom	wikipedia-en:Birkhoff–Grothendieck_theorem?oldid=1100877720&ns=0
page length (characters) of wiki page	4167 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Birkhoff–Grothendieck_theorem
is Link from a Wikipage to another Wikipage of	Birkhoff-Grothendieck theorem Holomorphic vector bundle George David Birkhoff Jumping line Birkhoff factorization List of theorems List of things named after Alexander Grothendieck Vector bundles on algebraic curves Grothendieck splitting principle
is Wikipage redirect of	Birkhoff-Grothendieck theorem Grothendieck splitting principle
is foaf:primaryTopic of	wikipedia-en:Birkhoff–Grothendieck_theorem

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