Monday, September 5, 2011

?? .... k[a:(x,x),b:(y-x,x),c:(-y,x),d:(-x,y),e:(x-y,y),f:(y,y)]/ad+be+cf ...

?? ideal generated by ac-eg .... ??? ..... ?? case g = infinity .... ???? ..... ???? case g = 0 .... ???? ....

?? also df-bg .... ???? .....

?? hmm, maybe we really want ideals homogeneous for both gradings ...

?? so ... maybe simplify a bit for the moment by just working with points instead of full flags ... so just a,b,c coordinates ...

?? hmm, but then .... ?? seems clear that there's a dense orbit ... ??? ...

?? frame for projective n-space given by generic (flag,flag,point) ?? .... ?? point as precisely (??) "calibrating aspect ratio" ?? ....

?? so ... ??? toric variety here ??? ...... projective n-space .... ?? "simplicial" fan .... ???? .... ?? n-simplex and [n+1]-cube ... ???? ..... ?? or perhaps [n+1]-diamond ?? ... ?? long axises of [n+1]-diamond corresponding to (max dim) faces of n-simplex .... ?? glueing technique for real spectrum of toric variety here .... ?? some poincare duality confusion here, but probably not bad ... ?? .....

?? blowing up to get full kaleidoscope toric variety ??? ..... ???? .....

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