Take the tour ×  Hello everybody! I would be interested in
knowing, what the reason is for investigating coherent sheaves
on complex manifolds. By definition a sheaf $F$ on a complex
manifold $X$ is coherent, when it is locally finitely presented
(i.e. every point possesses a neighborhood $U$, such that $F
\mid U$ is the image of $O_X^n\mid U$ under some surjective
morphism) and locally of finite presentation (i.e. for an open
súbset $U \subseteq X$ and a surjective morphism $f: O_U^n
\rightarrow F \mid U$ of sheaves the kernel of $f$ is locally
finitely presented). My question now is: Why are such sheaves
especially interesting? Why might somebody be interested in
studying them or what is the intuition behind them? Every help
will be appreciated.  share|improve this question Well, Oka's
coherence theorem says the structure sheaf of a complex manifold
is coherent...that's interesting. –  Keenan Kidwell May 1 at
23:51 It's the same reason that one develops a general theory of
finitely generated modules over no