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Subject Item
dbr:Tautological_bundle
rdf:type
yago:Collection107951464 yago:Package108008017 yago:Group100031264 yago:WikicatVectorBundles yago:Abstraction100002137
rdfs:label
Tautological bundle 보편 가역층 Tautologisches Bündel
rdfs:comment
In den mathematischen Gebieten der Topologie und Geometrie ist das tautologische Bündel auf einem projektiven Raum ein Objekt, das jedem Punkt die Gerade zuordnet, aus der er entstanden ist. In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of -dimensional subspaces of , given a point in the Grassmannian corresponding to a -dimensional vector subspace , the fiber over is the subspace itself. In the case of projective space the tautological bundle is known as the tautological line bundle. Tautological bundles are constructed both in algebraic topology and in algebraic geometry. In algebraic geometry, the tautological line bundle (as invertible sheaf) is 대수기하학과 미분기하학에서, 보편 가역층(普遍可逆層, 영어: universal invertible sheaf, tautological invertible sheaf) 또는 보편 선다발(普遍線다발, 영어: universal line bundle, tautological line bundle)은 사영 공간 위에 정의되는 표준적인 가역층(선다발)이며, 보통 로 표기된다. 대략, 사영 공간은 벡터 공간의 원점을 지나는 1차원 부분 벡터 공간들의 모듈라이 공간이므로, 보편 가역층은 사영 공간의 각 점에, 이 점이 나타내는 1차원 부분 벡터 공간을 대응시키는 선다발이다.
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dbc:Vector_bundles
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2913502
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1110446329
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dbr:Grassmannian dbr:Projective_bundle dbr:Addison-Wesley dbr:Linear_subspace dbr:Hopf_bundle dbr:Tautological_line_bundle dbr:Infinite_cyclic dbr:Grassmann_bundle dbc:Vector_bundles dbr:Relative_Spec dbr:Complex_projective_space dbr:Thom_spectrum dbr:Serre's_twisting_sheaf dbr:Characteristic_class dbr:Complex_field dbr:Fiber_bundle dbr:Disjoint_union dbr:Dual_bundle dbr:Line_bundle dbr:Mathematics dbr:Divisor_(algebraic_geometry) dbr:Chern_class dbr:Vector_bundle dbr:Exceptional_divisor dbr:Thom_space dbr:Algebraic_geometry dbr:Canonical_class dbr:Paracompact_space dbr:Bott_generator dbr:Möbius_strip dbr:Euler_sequence dbr:Invertible_sheaf dbr:Blowing_up dbr:Classifying_space dbr:John_Wiley_&_Sons dbr:Projective_space dbr:Dimension_(vector_space) dbr:Springer-Verlag dbr:Hyperplane_divisor dbr:Weil_divisor dbr:Algebraic_Geometry_(book) dbr:Homogeneous_coordinate dbr:Universal_bundle dbr:Canonical_(disambiguation) dbr:Linear_forms dbr:Vector_space dbr:Ample_line_bundle dbr:Algebraic_vector_bundle dbr:Dual_space dbr:Borel's_theorem dbr:Michael_Atiyah dbr:Proj dbr:Linear_functional dbr:Stiefel-Whitney_class dbr:Picard_group dbr:Direct_limit
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freebase:m.08c5_d dbpedia-ko:보편_가역층 dbpedia-de:Tautologisches_Bündel n17:2GFUP wikidata:Q2397465 yago-res:Tautological_bundle
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dbo:abstract
In den mathematischen Gebieten der Topologie und Geometrie ist das tautologische Bündel auf einem projektiven Raum ein Objekt, das jedem Punkt die Gerade zuordnet, aus der er entstanden ist. In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of -dimensional subspaces of , given a point in the Grassmannian corresponding to a -dimensional vector subspace , the fiber over is the subspace itself. In the case of projective space the tautological bundle is known as the tautological line bundle. The tautological bundle is also called the universal bundle since any vector bundle (over a compact space) is a pullback of the tautological bundle; this is to say a Grassmannian is a classifying space for vector bundles. Because of this, the tautological bundle is important in the study of characteristic classes. Tautological bundles are constructed both in algebraic topology and in algebraic geometry. In algebraic geometry, the tautological line bundle (as invertible sheaf) is the dual of the hyperplane bundle or Serre's twisting sheaf . The hyperplane bundle is the line bundle corresponding to the hyperplane (divisor) in . The tautological line bundle and the hyperplane bundle are exactly the two generators of the Picard group of the projective space. In Michael Atiyah's "K-theory", the tautological line bundle over a complex projective space is called the standard line bundle. The sphere bundle of the standard bundle is usually called the Hopf bundle. (cf. .) More generally, there are also tautological bundles on a projective bundle of a vector bundle as well as a Grassmann bundle. The older term canonical bundle has dropped out of favour, on the grounds that canonical is heavily overloaded as it is, in mathematical terminology, and (worse) confusion with the canonical class in algebraic geometry could scarcely be avoided. 대수기하학과 미분기하학에서, 보편 가역층(普遍可逆層, 영어: universal invertible sheaf, tautological invertible sheaf) 또는 보편 선다발(普遍線다발, 영어: universal line bundle, tautological line bundle)은 사영 공간 위에 정의되는 표준적인 가역층(선다발)이며, 보통 로 표기된다. 대략, 사영 공간은 벡터 공간의 원점을 지나는 1차원 부분 벡터 공간들의 모듈라이 공간이므로, 보편 가역층은 사영 공간의 각 점에, 이 점이 나타내는 1차원 부분 벡터 공간을 대응시키는 선다발이다.
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wikipedia-en:Tautological_bundle?oldid=1110446329&ns=0
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14273
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wikipedia-en:Tautological_bundle