Over a complex manifold, can every coherent sheaf be seen as a holomorphic vector bundle over an analytic subset?
Thanks in advance.
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 $X$.