?? idea that existence of non-affine toric variety can be interpreted as failure of certain naive generalization of certain "tannaka-krein" theorem from case of bicommutative hopf algebras to case of bicommutative bialgebras, and that such failure might be expected to persist beyond bicommutative case, giving examples of some sort of "non-affine generalized toric variety" ... ??? ....

?? was idly wondering whether this might relate to some concept of "generalized toric variety" (?? ...) that i think alex mentioned ben webster as having worked on ... maybe still wondering that, but may have changed my mind about relaxation of which half of bicommutativity might be involved ... ???

?? try glueing together oppositely "oriented" copies of m(2) along common gl(2) ?? .... ???? .....

?? particularly possibility of _"projective"_ (??? .... ???? ....) generalized toric variety here .... ???? .....