?? "auto-skin-graft" metaphor (for "ordinary" geometric interpretation of "non-snug cone inclusion" in fan picture ... ??? ...) as weird because ... ??? arguably there is donor and recipient, and they're not the same .... ???? ... ??? still, vague idea of "one location benefit at expense of other" seems to apply somehow ... ??? .... ?? hmm, maybe the single patient is supposed to be something like the torus ?? ... ??? ...

?? moment ago were toying with "blow-up" being canonical only for codimension one, but now back to thinking that it(?? ...)'s always canonical ... ??? "ideal power filtration" .... ???? .... ??? .... (?? vague memory of some uncertainties that we had about that though ... i mean some pretty minor ones, about intersection of ideals vs pullback of associated modules over 1, or something like that ????? ....... not the major ones about ... some attempted big picture ... ??? ...) ?? though is the toric structure canonical ????? ..... ???? .... not completey sure yet ... something's got to give .... ??? ......

?? when fan cone gets "too big" (?? meaning zero's in convex hull of rest ?? ...) doesn't so much "disappear" as "collapse to point" ... ???? ... ?? wait, does that make any sense ??? ..... ?? corresponding co-fan co-cone .... ???? .... ?? vague memory about "co-fan co-cone "loses" dimension by becoming invariant in it" ... ???? ?? yes, but now we're considering "non-admissible" co-cones (not generating the whole co-fan lattice), and the corresponding "non-admissible cone" does seem like it could be construed as quotient .... ??? actually i'm probably confused enough here that i shouldn't trust what i'm saying yet .... ??? .... ?? should straighten out ?? ....

?? toric singularity ... ?? .... cone ... checkerboard ... ??? ....

??? so i think that i do remember now thinking a bunch about "blow-down" and "ideal as sub-rng" ... on a particular day when a bunch of that stuff really seemed to make sense, or threaten to do so ... ?? what was that idea about "universal way of making a subvariety a cartier divisor", or something like that ??? ... ?? some adjoint functors here .... ??? some vivid mental pictures involving curve in 3-space .... ???? ..... hmmm .... ?? but i don't offhand recall thinking about how ... ?? ... ?? when you blow down a subvariety of an affine variety, the bit about "subring inclusion as roughly corresponding to quotient map, but often not quite surjective" may bite ... ??? so that when you blow-up again you may get something projective (?? ...) extending / completing (?? ...) the original affine variety ... ????? .....

?? knot invariant coming from invariant of its blow-up ??? .... ???? ....

?? hmmm, so ... ?? issue of compatibility of blow-_down_ with toric structure ... ??? .... ?? and ... ?? canonicalness of toric blow-down ... ??? ....

??"knocking out wall ..." ... ??? of cone, vs of co-cone ... ??? ... ?? alleged canonical result here as generally "too big" ??? .... ???? ....

?? again, sure we thought about this to _some_ extent before, but ... ?? how sharp is paradox here involving .... ???? ..... "non-singular" ways of subdividing standard lattice quadrant ... ??? ... ?? hmm, maybe quite dull rather than sharp ... ?? usual bit about invertibility of aut(n) -> aut(free comm monoid(n)) ?? ....

?? "toric (??prime ?? ...) ideal" as wall complement ... ??? .... ?? or face complement ........ ???? .... ???? .... ?? hmmm, is there a somewhat nice picture here of "specialness of co-dimension one" here ??? .... ?? wall complement as "_minimal_ prime" ideal ... ??? ....