Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
The determinant bundle of a vector bundle E is the top exterior power of E.
|
| gptkbp:field |
gptkb:Algebraic_geometry
gptkb:Differential_geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
Determinant bundle
|
| gptkbp:notation |
det(E)
|
| gptkbp:property |
The determinant bundle is functorial with respect to pullbacks.
If E is a rank n vector bundle, det(E) is a line bundle. |
| gptkbp:relatedTo |
gptkb:Picard_group
gptkb:Vector_bundle Line bundle Determinant line bundle |
| gptkbp:usedIn |
gptkb:Index_theory
gptkb:gauge_theory gptkb:Algebraic_curves Moduli spaces |
| gptkbp:bfsParent |
gptkb:Vector_bundles_(in_algebraic_geometry)
|
| gptkbp:bfsLayer |
7
|