??? toric variety from graded object ... ??? ....

?? augmentation ... ??? bialg counit ?? .... ??? ....

?? ....

?? process involving modding out by homogeneous ideal .... ??? why not just "mod out by it ahead of time" ?? .... ???? ..... ??? property .... ????? .....

???? ... "zariski closure of torus orbit" ... ??? .....

"homogeneous core" ....

?? so ... various (?? generalized ??) properties of dimensional algebra ... (?? or of AG theory under AG theory coming from discrete abelian group, maybe later ... ?? ....)

?? being monoid algebra, with grading group being its groupization ...

?? being bialgebra ... ??? .... ??? "augmentation" ... ???? ....

?? "spectrum having dense orbit" .... ????? .......

??? grades being small .... ??????....

??? vague idea about "superimposing multiple orbits" .... ?????.......