Given a graded ring $S$ and a graded $S$-module $M$ there is a sheaf associated to $M$ on Proj $S$.
What is the best way to think of the corresponding situation in the complex analytic setting? I.e., if $M$ is a $\mathbb{C}[z_0,\dots,z_n]$-module, is it possible to associate $M$ to an $\mathscr{O}_{\mathbb{P}^n}$-module, where $\mathscr{O}_{\mathbb{P}^n}$ is the sheaf of holomorphic functions on $\mathbb{P}^n$?