??so... a "projective embedding" sort of corresponds to a line bundle... ??so then for example what sort of "system of line bundles" does an "embedding into a grassmanian of 2d linear subspaces" correspond to?? ... (or something like that... ??what about "what sort of system of line bundles does a bundle of 2d vector spaces correspond to?" ?? .... ???) ...in a way this seems like a very straightforward question, but... ??nevertheless it seems like thinking about it should be illuminating in certain ways... relationships between "algebraic geometry" and "homotopy theory" or something... ??and so forth??...

??something about "representation theory" too ... ??...

??what about also "multi-projective embedding" here?? ... and so forth... ??or something... ???....

??what about the idea of "harmless extra structure" here?? ...or something like that... ???....

??so ... ??we have a sort of quasi-algorithm that given a line bundle produces a projective embedding: something like: take the vector space of sections of the bundle, and embed into it in the hopefully obvious way... ??or something?? (something about divisor of a point here?? something about "divisor" vs "ideal" ??? .... ???....) ??so then what's the corresponding quasi-algorithm that, given a 2d vector bundle, produces an embedding into a grassmanian of 2d linear subspaces?? ... well, so somehow we should obtain a vector space whose grassmanian of 2d vector spaces would be just the thing to contain an embedded copy of our base space... ???so what _is_ this how??... ??how about the vector space of all sections of the 2d vector bundle?? or something?? so given a point of our base space, assign to it the subspace of sections that vanish at that point... ??what dimension should that subspace be??

at the moment we seem to be doing a fairly good job of making things that should (i think...) be familiar seem exotic... ???...

???what about sections of a vector bundle that vanish on some higher-dim variety?? ....

??....

??"divisor" as "holomorphic structure" on (??standard??) "meromorphic line bundle" .... ????...

???so what about something about "birational geometry" and "flatness" ??? .... or something ... ???...

??what's a "holomorphic structure on the standard meromorphic 2d vector bundle" ??? ... ??or something???.....