?? non-toric analog of fan for certain reasonably nice sort of variety ... ??? pasted together from affine spectrums of subrings of field of meromorphic functions on the variety .... ????? ...... ???? "closure of generic point as entire variety" ... ???? .....

?? maybe trying to use this to approach those certain questions about non-toric analogs of theorems about how un-general TAG theories of toric quasicoherent hseaves (?? ...) are ... ????....

?? "holomorphic structure on meromorphic line bundle / vector bundle" ... ???? ....

?? "divisor" ... ???? .... ?? ....

?? maximal variety based on given field .... ????

?? analog of "no two cones in fan overlap in cone of nonzero volume" ??? .... ????....

?? blow-up as giving (?? toric or non-toric ... ?? ...) birational equivalence ... gluing variety and blow-up of it together ... ??? whether blow-up "supersedes" original ... ???? .... ?? confusion about fan ... ??? ... ??? "geometric colimit" ... hmmm .... ???? .... ?? original as superseding blow-up then ??????? .... ???? .....

??? geometric monic ... ????? .... ?? blow-up .... ???? .... ?? localization as automatically geometrically monic ... ??? .... ??? but ... ??? ... ??? .... ??? ...

?? dimensional category where all nonzero quantities are invertible ??? ... ??? toric analog as tame stable 2-type ... ??? .....

?? _is_ toric variety birationally equivalent (in ordinary sense ...) to its torus ?? .... ???? .....

?? getting toric dimensional category from fan ???? .....

?? wpa says:

The toric variety of a fan is given by taking the affine toric varieties of its cones and glueing them together by identifying Uσ with an open subvariety of Uτ whenever σ is a face of τ.

?? ... ??that seems to leave possibility of one cone in fan being contained in another without any face relationship ... ???? ?? is that really what they want ??? ?? does it give "separated" thing ? ... ???? ....

?? "delocalizations" of given field / torus (in toric case ...?? ...) ?? .... ???category of such delocalizations ??? .... ??? as forming lattice ??? ... ??? .... ??? .... ?? morphisms between elocalizations as ... ???? ....

?? thought for a moment that it might make sense for toric variety to be "[truth-value]-valued sheaf" (?? ...) here ... ??? ..... ???? ..... ??? ...

?? hmm, maybe it _does_ ?? ... ??? ... ?? encoding downward-closed subcollection as something like "anti-chain" ... only include irredundant generators ... ??? ....

?? kind of equivalence (??? ...) of diagrams for purposes of taking co-/limits ... ??vaguely reminds me of kind of equivalence between graphs (?? ...) involved in theorem about planarness .... ?????? ..... "subdivision ... " .... ??? ...

?? "locale of localizations" vs ... ??? "delocale of delocalizations" ??? ... ???? ....

?? localizations of x as part of delocalizations of x' = "spectrum of field of meromorphic functions on x" ??? .... ???? ....

?? but delocalizations of x' as forming poset that's some sort of union of posets of "poset of localizations" kind but not of that kind itself ??? .... ??? .... ?? maybe need some sort of (??co-)completion process ?? ... ??? .... ?? maybe some sort of hopefully obvious "canonical" (?? ...) grothendieck toplogy on category of delocalizations ... ??? ...

?? don't forget ... ??? previous attempts of ours to push analogy of ordinary varieties to toric varieties, emphasizing delocalizations (i think ... though not under that name ... ??? ....) ... "frankenstein doctrine" ideas ??? .... ???? ....