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Tautological bundle

In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of k {\displaystyle k} -dimensional subspaces of V {\displaystyle V} , given a point in the Grassmannian corresponding to a k {\displaystyle k} -dimensional vector subspace W ⊆ V {\displaystyle W\subseteq V} , the…

Standards, Tautological line bundle in algebraic geometry & Overview

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Intuitive definition

Formal definition

Hyperplane bundle

Tautological line bundle in algebraic geometry

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Map overview Semantic statistics

Tautological bundle

Nodes75
Edges74
Triples26
Avg. degree1.97
Density0.026667
Components1

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Tautological bundle

Top relations

related to Intuitive definition · 9
Tautological bundle → All, By, Fixing, Grassmannian, Grassmannians, If, That, The, With
related to Formal definition · 8
Tautological bundle → Cartesian, Finally, For, Grassmannian, If, Let, The, We
see also · 7
Tautological bundle → Borel's, Chern, Grassmann, Grassmannian, Hopf, Thom, Whitney
is a · 2
Tautological bundle → line bundle, vector bundle occurring over a Grassmannian in a natural tautological way

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Important terminology

bundle tautological displaystyle line space mathbb vector algebraic geometry grassmannian projective hyperplane dual bundles given sheaf divisor corresponding called definition

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Tautological bundleis avector bundle occurring over a Grassmannian in a natural tautological way0.90text
Tautological bundleis aline bundle0.90text
Tautological bundlerelated to Formal definitionLet0.60section
Tautological bundlerelated to Formal definitionGrassmannian0.60section
Tautological bundlerelated to Formal definitionFor0.60section
Tautological bundlerelated to Formal definitionWe0.60section
Tautological bundlerelated to Formal definitionThe0.60section
Tautological bundlerelated to Formal definitionCartesian0.60section
Tautological bundlerelated to Formal definitionIf0.60section
Tautological bundlerelated to Formal definitionFinally0.60section
Tautological bundlerelated to Intuitive definitionGrassmannians0.60section
Tautological bundlerelated to Intuitive definitionIf0.60section

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    Min side: 3
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