Let $X$ be a scheme, and let $l$ be a line bundle on $X$. What can we say about the line bundle $l$ that will make $X$ projective? Or is there nothing one can say?
If this fails, how can we characterize a projective scheme in terms of its bundles?
I am interested since I want to know the bundle-theoretic significance of projective space. This should also be related to intersection theory on projective space, via the Grothendieck-Riemann-Roch theorem.