Let $X$ be a smooth projective variety and let $F$ be a torsion free coherent sheaf. We then have an injection $F\hookrightarrow F^{\vee\vee}$. Let $C$ be the cokernel of this injection. I believe $C$ is torsion.
I remember a statement saying that $C$ is supported only in codimension $\geq 2$. Is this a true statement? If so, is there a reference?
I am aware of Karl Schwede's note's on reflexive sheaves, but could not find the statement I want.
Thanks a lot!