# A coherent sheaf is a vector bundle over subvariety?

Over a complex manifold, can every coherent sheaf be seen as a holomorphic vector bundle over an analytic subset?

Let $$I$$ be the ideal sheaf of a point $$p$$ in $$X=\mathbf A^2$$. On the complement of $$p$$, the sheaf $$I$$ is equal to the line bundle $$O_X$$. But two line bundles which are isomorphic on an open subset $$U \subset X$$ whose complement has codimension at least 2 must be isomorphic on $$X$$.