?? so we've got this idea now that .... the idea of "blowing up a sub-variety" is actually very tightly connected with the whole idea of interpreting a sub-variety as an ideal (or more generally... that is in the non-affine case ... ??well, simply sub-variety ??? ... ??? ...) in the first place ... or perhaps i should emphasize more with taking the _underlying module (??or more generally line bundle?? ...)_ of the ideal ... in the sense that this module is "a lot like the unit module away from the sub-variety, but blown-up over the sub-variety" ...

(??? idea of "blowing up a module at an ideal" ??? .... ??? does anything like this parse??? hmmm, maybe just tensoring the module with the ideal ??? .... ??relationship to tensoring the module with the symmetric algebra of the ideal ??? .... ????? ....)

?? but ... ??something a bit funny here ... worth understanding most likely ... ???that in the case where the module is invertible, the effect of blowing-up is supposed to be vacuous, right?? ... whereas ... notoriously not all such invertible modules are equivalent as modules to the unit module ... so ... seems to be something like ... ??all invertible modules have equivalent symmetric algebra, though are not themselves all equivalent ... ??? .... ??so there should be an interesting variety of ways in which you can take the symmetric algebra of the unit module and find inside of it alternative free generating submodules .... ????? ??am i saying this right ???

???underlying affine scheme bundle of line bundle as always trivial ??? .... .... ???putting line bundle structure back on it as thus interesting?? ... ???or as in contrast of course (??) just trivial ... ???

?? so now it seems like i've got some obvious paradox, so probably screwed up somewhere ... so definitely try to straighten this out ... ???

???hmmm, well ... there is obvious fact that ... of course the "linear" structure _can_ be modified ... namely by changing origin ... ????so is _that_ what's going on here ?????? ...... hmmmm ...... ?????...... ??seems like attractive idea, but ... ???? in danger of believing that choosing section of trivial line bundle amounts to ..... ?????? ... ???choosing non-trivial line bundle ???? ..... sounds ... almost but not quite right-track ??? .... ???? ..... ???? ....

??relationship between "underlying affine scheme bundle as trivial" and "underlying meromorphic line bundle as trivial" ??? .... ???? .... ???? ....

??vague memory about .... ????coherent sheaf cohomology ... affine space as short exact sequence ... ???????..... ?? h^2 ... ??? ....