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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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bundle tautological displaystyle line space mathbb vector algebraic geometry grassmannian projective hyperplane dual bundles given sheaf divisor corresponding called definition
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Tautological bundle | is a | vector bundle occurring over a Grassmannian in a natural tautological way | 0.90 | text |
| Tautological bundle | is a | line bundle | 0.90 | text |
| Tautological bundle | related to Formal definition | Let | 0.60 | section |
| Tautological bundle | related to Formal definition | Grassmannian | 0.60 | section |
| Tautological bundle | related to Formal definition | For | 0.60 | section |
| Tautological bundle | related to Formal definition | We | 0.60 | section |
| Tautological bundle | related to Formal definition | The | 0.60 | section |
| Tautological bundle | related to Formal definition | Cartesian | 0.60 | section |
| Tautological bundle | related to Formal definition | If | 0.60 | section |
| Tautological bundle | related to Formal definition | Finally | 0.60 | section |
| Tautological bundle | related to Intuitive definition | Grassmannians | 0.60 | section |
| Tautological bundle | related to Intuitive definition | If | 0.60 | section |
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