Projective geometry was introduced by fifteenth century Renaissance painters (like Alberti, da Vinci and Dürer) in the guise of perspective theory, although one could argue that Pappus was already doing projective geometry in the fourth century A.D.

Projective geometry was formalized as a synthetic geometric theory by Desargues around 1640, but coordinate projective geometry was introduced by Plücker only in 1830 in his article *Über ein neues Coordinatensystem* in the recently created *Journal für reine und angewandte Mathematik*.

In 1955 Serre described, in his ground-breaking article *Faisceaux Algébriques Cohérents*, a remarkable technique associating to a graded algebra $S$ a projective variety $Proj(S)$ and to a graded $S$-module $M$ a quasi-coherent sheaf $\tilde M$.

**Here is my question:**

Since Serre's technique is *a priori* so counterintuitive, I was wondering if there are previous publications hinting at the link between graded rings and projective algebraic geometry.

I'm hoping for some precursor, analogous to the introduction by Gel'fand of the spectrum of a $C^*$-algebra announcing Grothendieck's construction of an affine scheme associated to a completely arbitrary commutative ring.

**Edit**

After reading the comments I think I should clarify what I'm after:

it was indeed probably well known before Serre that one could associate to a projective variety $X\subset \mathbb P^n$embedded in $\mathbb P^n$ its graded coordinate ring $S(X)$: this is pretty easy once one has the concept of graded ring.

What I find much more difficult is to associate to a graded module of finite type over $S(X)$ a coherent sheaf and in particular to see line bundles on $\mathbb P^n$ as obtained from the twistings of a polynomial ring.

I am **sure** that nobody did that before Serre because **nobody** before him had even considered coherent sheaves on algebraic varieties endowed with the Zariski topology!

So my question is not whether someone found that correspondence before Serre (nobody did) but whether someone was, with the benefit of hindsight!, on the right track.

Also I would be grateful for precise references: with schemes and sheaves taught today more or less in Kindergarten it is easy to underestimate the audacity of some constructions at a time when sheaves had just been discovered (even their definition was in constant flux) and when homological algebra was a brandnew technique.