i said :

?? dimensionality aspect of delocalization poset ??? .....

?? for example, delocalizations of rational functions in 2 variables .... ???? .... ??? analog of "2d (??limiting case??) fan containing all rays" ?? .... ??? ....

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hmmm ... ?? local rings of irreducible subvarieties of various dimensions .... ????? .... ??? "multi-local" rings of reducible subvarieties ??? .... .... ????? ....

??? toric analog ?????? ..... ????? .... ??? "local commutative monoid" .... ???"prime ideal" in commutative monoid ?? .... (?? visual intuition about cocone face associated to cone face ... ????) .... ?? seems like this (...) is probably well-known; in particular that stuff i bumped into once that i only vaguely remember .... ?????..... ??? whole bunch of things to try with this .... ??? for example toric analogs of topos stuff occurring in ordinary algebraic geometry ?? ... tierney "spectrum" stuff ... ??? .... ??? ....

???any possibility of .... polytope : toric de-/localization :: "q-deformed polytope" : some kind of non-toric de-/localization ??? .... ???? .....

?? toric line bundles (???? ....) over kaleidoscopic toric variety vs line bundles over flag variety ??? ..... ??? ..... ???? .....

??? relationship between "local" and "nilpotent" here ????? .... ????? ......

??? aspects of "filtered" which live in toric context ... ??? vs other aspects ?? .... ?? "associated graded ..." ... ???