??hmmm, let me think outloud about this a bit ...
inverting a morphism in an ag theory which is not a coequalizer ...
??hmmm, not clear how to include case of removing higher codimension variety here ... ??or something?? ... ?????hmmm, what about idea of ... ???removing by [blowing up, followed by removal by localization] ?? ... ??or something ?? ... ????hmmm, any relationship to "adding extra stuff" ??? ... hmmm... not clear ... ???? .... because we only seem to be adding a line object under this scenario ... ??or something ???...
??what about something about top exterior power here, or something ?? ...
??something about funny tradeoff, or something ?? ??extra stuff, for being able to remove higher co-dimension subvariety ... ??or something ?? ...
anyway, back to ... ???something about ... ??"trying to force at least one of a pair of functions to take on an invertible value" ... ??? ??or something ???....
??ideal power filtration ... ???....
?? "extra line object with structure amounting to a canceling scale except on a closed (and perhaps higher co-dimension ...) subvariety " ... ??...
???hmm, might there be an "infinite regress" problem here ??? ??or something ??? ... ??each new line bundle that you introduce as requiring fixing ... ??is this just a silly way of pushing the problem over the horizon, or what ??...
well, so let's try it anyway... ??maybe to try to find out whether there's an infinite regress or something ...
polynomials in 2 grade 0 variables x,y ... ??...
??then consider ideal power filtration for
??something about simply ... ???adjoining inverse for underlying module of ideal ??? ... ??or something ???? .... ...?? we're supposed to know all about thsi already, right ?? ... ???...
??"a pair f,g of functions equipped with an inverse for the cokernel of (f,g) : 1 -> 1+1" ... ??? or something ... and so forth ....
??i'm getting a bit confused about what this is supposed to do ... blow up a sub-variety, or remove it, or what ... ???
??also are we taking advantage of special aspect of 2d case here ??? ... and so forth ... ??...
???something about inverse for _ideal_ .... ???hmm, so how do you get your handson that??? ... and ... ???this as probably pretty much how martin solved the problem ??? ... ???or something .... ??? ....
??so... if adjoining inverse ideal is supposed to remove the sub-variety (or something...), then what _about_ the other thing that's just supposed to blow it up ?? ... well, so it's got something to do with "taking the ideal power filtration and interpreting the filtered object _as_ a graded object with extra structure ... " ... ???but there must be a way more conceptual way of thinking about it ... that at least on good days we must already have sort of understood ... ??...
??something about ... ???"inverting the inclusion-in-next-stage operator" (?? =?= "scaling parameter" ??? ... =?= "scale" ??? or something?? ...)... ???as ... giving the "scaling-deformed" object ??? ... ???and so forth ... ???... ??what about inverting vs setting to 1 here ??? or something??? hmm, maybe sort of doesn't parse, or something... or vacuous.... something about inverting it as what allows you to "pretend that it's 1" ... ???or something ... ???...
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