?? projective n-space as toric variety ... ?? "theory (?? of doctrine "ag + toric convolution" .... ??? ...) of line object x equipped with nice embedding into standard [n+1]-space, plus toric convolution cocommutative comonoid structure on x ..." .... ????? .....

?? why did brandenburg mention "locally free" at all ??? .... ... bad sign .... ???? .....