A reflexive sheaf (i.e its double dual is equal itself) is locally free (i.e., a holomorphic vector bundle) outside a subvariety of codimension greater than or equal to two. Let $\mathcal F$ be a coherent subsheaf of holomorphic vector bundle $E$, then there is an analytic subset $S \subset M$ of codimension bigger than two and a holomorphic vector bundle $F$ on $X \setminus S$ such that $$\mathcal F|_{X\setminus S}=\mathcal O(F)$$

We know that a reflexive sheaf $\mathcal F$, on Kahler variety $X$ outside of codimension at least 3 is a holomorphic vector bundle,

Under which condition such singular variety $S$ is an analytic sub-variety?