About: Holomorphic vector bundle

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In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold X such that the total space E is a complex manifold and the projection map π : E → X is holomorphic. Fundamental examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphic cotangent bundle. A holomorphic line bundle is a rank one holomorphic vector bundle.

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rdfs:label	Holomorphic vector bundle (en) 정칙 벡터 다발 (ko) 正則ベクトル束 (ja) Fibrado vetorial holomórfico (pt) 全纯向量丛 (zh)
rdfs:comment	数学において，正則ベクトル束（せいそくベクトルそく，英: holomorphic vector bundle）とは，複素多様体 X 上の複素ベクトル束であって，全空間 E が複素多様体であり射影 π: E → X が正則であるようなものである．基本的な例は複素多様体の正則接束とその双対正則余接束である．正則直線束 (holomorphic line bundle) は階数が 1 の正則ベクトル束である．セールの GAGA により，滑らかな複素射影多様体 X（複素多様体と見る）上の正則ベクトル束の圏は，X 上の（すなわち階数が有限の局所自由層）の圏と同値である． (ja) 미분기하학에서 정칙 벡터 다발(正則vector다발, 영어: holomorphic vector bundle) 또는 해석적 벡터 다발(解析的vector다발, 영어: analytic vector bundle)은 복소다양체 위에 정의된, 사영 사상이 정칙 함수인 복소수 벡터 다발이다. (ko) Em matemática, um fibrado de linhas holomórfico é um fibrado vetorial complexo sobre uma variedade complexa X tal que o espaço total E é uma variedade complexa e o mapa de projeção é holomórfica. Especificamente, requer-se que os mapas de trivialização são . Isto é equivalente a requerer que as funções de transição são mapas holomórficos. Um fibrado de linhas holomórfico é um fibrado vetorial holomórfico de ordem um. (pt) 数学上，全纯向量丛是指一个在复流形X上的复向量丛，其全空间E为一复流形，丛投影是全纯的。重要的全纯向量丛包括复流形上的全纯切丛，以及其对偶全纯余切丛。一阶全纯向量丛也称作全纯线丛。全纯向量丛的平凡化映射为。即等价于转换函数为全纯映射。 (zh) In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold X such that the total space E is a complex manifold and the projection map π : E → X is holomorphic. Fundamental examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphic cotangent bundle. A holomorphic line bundle is a rank one holomorphic vector bundle. (en)
rdfs:seeAlso	Dolbeault cohomology Hermitian connection
dcterms:subject	Complex manifolds Vector bundles
Wikipage page ID	4794668 (xsd:integer)
Wikipage revision ID	1037945825 (xsd:integer)
Link from a Wikipage to another Wikipage	Complex manifolds Holomorphic function Curvature form John Wiley & Sons Ringed space Connection form Mathematics Quillen metric GAGA Connection (vector bundle) Closed and exact differential forms Complex differential form Complex manifold Complex vector bundle Partition of unity Vector bundles Exact sequences Parallel transport Sheaf extension Projective variety Tensor product Abuse of notation Birkhoff–Grothendieck theorem Coherent sheaf cohomology Holomorphic tangent bundle Nakano's vanishing theorem Dolbeault's theorem Inner product Chain complex Topological manifold Sheaf (mathematics) Algebraic vector bundle Hermitian metric Sheaf cohomology Glossary of algebraic geometry Transition map Vector valued form Biholomorphic map Fine sheaf Newlander-Nirenberg theorem Projection map Smooth variety Baer sum Holomorphic cotangent bundle Kodaira's vanishing theorem Locally free sheaf Structure sheaf
Link from a Wikipage to an external page	https://mathoverflow.net/q/87719
sameAs	Holomorphic vector bundle Holomorphic vector bundle Holomorphic vector bundle Holomorphic vector bundle Holomorphic vector bundle Holomorphic vector bundle Holomorphic vector bundle Holomorphic vector bundle
dbp:wikiPageUsesTemplate	dbt:Springer dbt:! dbt:Citation dbt:Math dbt:Mvar dbt:Reflist dbt:See_also
id	v/v096400 (en)
title	Vector bundle, analytic (en)
has abstract	In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold X such that the total space E is a complex manifold and the projection map π : E → X is holomorphic. Fundamental examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphic cotangent bundle. A holomorphic line bundle is a rank one holomorphic vector bundle. By Serre's GAGA, the category of holomorphic vector bundles on a smooth complex projective variety X (viewed as a complex manifold) is equivalent to the category of algebraic vector bundles (i.e., locally free sheaves of finite rank) on X. (en) 数学において，正則ベクトル束（せいそくベクトルそく，英: holomorphic vector bundle）とは，複素多様体 X 上の複素ベクトル束であって，全空間 E が複素多様体であり射影 π: E → X が正則であるようなものである．基本的な例は複素多様体の正則接束とその双対正則余接束である．正則直線束 (holomorphic line bundle) は階数が 1 の正則ベクトル束である．セールの GAGA により，滑らかな複素射影多様体 X（複素多様体と見る）上の正則ベクトル束の圏は，X 上の（すなわち階数が有限の局所自由層）の圏と同値である． (ja) 미분기하학에서 정칙 벡터 다발(正則vector다발, 영어: holomorphic vector bundle) 또는 해석적 벡터 다발(解析的vector다발, 영어: analytic vector bundle)은 복소다양체 위에 정의된, 사영 사상이 정칙 함수인 복소수 벡터 다발이다. (ko) Em matemática, um fibrado de linhas holomórfico é um fibrado vetorial complexo sobre uma variedade complexa X tal que o espaço total E é uma variedade complexa e o mapa de projeção é holomórfica. Especificamente, requer-se que os mapas de trivialização são . Isto é equivalente a requerer que as funções de transição são mapas holomórficos. Um fibrado de linhas holomórfico é um fibrado vetorial holomórfico de ordem um. (pt)

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