A line bundle is a special case of a vector bundle in which the fiber is either 
, in the case of a real line
bundle, or 
,
in the case of a complex line bundle.
In algebraic geometry, a line bundle on a scheme 
is a locally free sheaf
of 
-modules
of rank one, where 
is the structure sheaf. Equivalently, it is an
invertible 
-module, or invertible sheaf
(The Stacks Project Authors 2026). Its isomorphism
class is an element of the Picard
group of 
.
