???so.... punctured plane as toric variety ... fan as "boundary of quadrant" in Z^2 ... ????....

????relationship to projective line??? ....????visual relationship of fans ??? .... ??? ...

???fans with "overlay" aspect ??? .... ???relationship to "non-separated toric pre-scheme ...." ???? .... ??? .....

?"0-subvarieties" vs "1-subvarieties" of toric varieties, and different conceptual roles they play ?? .... ???1-subvariety as actual "subvariety", 0-subvariety as "fringe" ??? ... ??? .... ???but then ... ???distinction blurred or erased with "toric geometry with 0" ?? ... ??? ..... ??application to "associated graded" ??? ... ???whether ag morphism for which "associated graded" acts as geometric pullback qualifies as toric or generalized toric .... ??? ... ???...

???orbit _toric_ stack of toric variety wrt _the_ torus ??? .... ????? .... ??? .... ?? affine line as example .... ????toric quasicoherent sheaf over orbit stack as "generalized filtered set" = "Z-tree" ???? .... ?????..... ??tensor product of Z-trees ...

???quasito(r)pos of _genuine_ filtered sets ??? .... .... ???....


????cohomology of toric quasicoherent sheaf ... ??? .... ??? ???cohomology of quasicoherent sheaf over toric variety .... ??? .... frankenstein ... cover ... glueing ... ?? ....

???frankenstein _non_-doctrine ??? ...

???toric geometry as playground for ... ???..... "cohomological approach to local geometry of moduli stack" ... ??? .... "deformation theory" ... "rational homotopy theory" ... ??? .....


???role of gl(n,Z) (??? ...) in connection with fans on Z^n (...??...) vaguely reminding me of maybe similar role in connection with ... ??? ???root system ... weight diagram ... "character" .... "chern-weil" ... ???? ... ????.....

??toric structure on projective plane (for example ...) and "kaleidoscope as fan" ... ???? ....

???tendency for toric geometry (??...) to "stay under wildness threshold" ??? ....

kaleidoscope as fan .... ???? maximal torus .... ??? ....