line bundle
In algebraic geometry, the term line bundle refers to a locally free coherent sheaf of rank 1, also called an invertible sheaf. In manifold theory, it refers to a real or complex one dimensional vector bundle. These notions are equivalent on a non-singular complex algebraic variety : given a one dimensional vector bundle, its sheaf of holomorphic sections is locally free and of rank 1. Similarly, given a locally free sheaf of rank one, the space
given the coarsest topology for which sections of define continuous functions in a vector bundle of complex dimension 1 over , with the obvious map taking the stalk over a point to that point.
Title | line bundle |
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Canonical name | LineBundle |
Date of creation | 2013-03-22 13:31:04 |
Last modified on | 2013-03-22 13:31:04 |
Owner | bwebste (988) |
Last modified by | bwebste (988) |
Numerical id | 5 |
Author | bwebste (988) |
Entry type | Definition |
Classification | msc 14-00 |