1
$\begingroup$

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

Thanks in advance.

$\endgroup$
2
$\begingroup$

No.

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 $X$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.