2
$\begingroup$

Let $X$ be a compact complex manifold and $\mathcal{F}\to X$ a sheaf.

Is there a regularity criteria (or a condition) for $\mathcal{F}$ that determines whether we there exists a closed subvariety $i:Y\hookrightarrow X$ and a locally free sheaf $\mathcal{G}$ such that $\mathcal{F}=i_*\mathcal{G}$?

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ The natural choice for $Y$ will be the scheme-theoretic support of $\mathcal F$. Do you have something in mind for the $Y = X$ case? $\endgroup$
    – red_trumpet
    May 26, 2022 at 16:53

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.