Reflexive sheaf

The notion is important both in scheme theory and complex algebraic geometry.

For the theory of reflexive sheaves, one works over an integral noetherian scheme.

A coherent sheaf F is said to be "normal" in the sense of Barth if the restriction

[2] A reflexive sheaf of rank one on an integral locally factorial scheme is invertible.

[3] A divisorial sheaf on a scheme X is a rank-one reflexive sheaf that is locally free at the generic points of the conductor DX of X.