nLab
line bundle

A line bundle is a vector bundle of rank (or dimension) $1$, i.e. a vector bundle whose typical fiber is a $1$-dimensional vector space (a line?).

The class of line bundles has a nicer behaviour (in some ways) than the class of vector bundles in general. In particular, the dual? of a line bundle $L$ is a weak inverse of $L$ under the tensor product of line bundles. Thus the isomorphism classes of line bundles form a group.