Invertible sheaf

Summary

An invertible sheaf on a ringed space is a sheaf of modules that is locally isomorphic to the structure sheaf. It is the algebraic version of a line bundle, a family of one-dimensional vector spaces over the points of the space. The name comes from the fact that, on a scheme, such sheaves are exactly the sheaves of modules with an inverse for the tensor product. Their isomorphism classes form the Picard group.