?? so ... when you blow up a point (??) on a toric variety / subdivide co-dim 0 (??) cone in fan ..... ???? ..... the new subvariety as ... ??? maybe not precisely a toric variety .... ???? .....???? .... ???? .... ?? bit about various sorts of ideals of interest .... ???? ..... generated by toric functions vs by equations between such ... ??? .....

?? might the subarieties which don't especially seem like they "should" (?? corresponding to ideals generated by single toric functions ... ??) be nevertheless "accidentally" toric after all ?? .... ??? or "generalized toric" ... ??? ....

??? "generalized fan" ... ??? as maybe somewhat clear from discussion about "non-linear fan" ... ???? ....

??? various ways of subdividing cone, vs ... ?? ess just one way to blow up point .. ??? .... ????? .....

?? blowing up a higher dim (??? good ???) subvariety on a toric variety ... ???? .... ?? subdividing higher-dim cocone in cofan ... ????.... ??? ....