?? so consider .... ???? ideal power filtration of the ideal generated by x and y in k[x,y]/x^3-y^2 .... ????.....

???? ...... ???? .... ??? ... hmmmm .... ideal power filtration of non-principal ideal .... ????? ......

??? confusion .... ????? ...... 0,23,45,67,... ???? .... ??? idempotent ideal ?? .... ?? exotic (?? ...) instances of associated graded alg of ideal power filtration .... ???? ...

?? associated graded ... ????.... ??? vs zariski tangent space .... ????? ...... ???? .....

??? have we thought about this before and forgot, or ... ??? ...

??? certainly we've thought about "double point" singularity ... ???? ?? this as degeneration of that ???? ....... hmmmm ....

??? "co-unit ideal" of monoid alg of comm monoid .... ???? .....

?? "filtered commutative monoid" .... ???? ...... ???? any relationship to what ben-zvi mentioned about carlos simpson ?? .... ????? .......

???? associated graded comm monoid of filtered comm monoid ... ??? .... ?? hmm, evidently the associated graded alg of a filtered comm monoid algebra isn't a monoid algebra in general ... ????...... ?? not that far off though ??? ..... ?? for some reason vaguely reminds me of ... ??how did that go .... ???"zero as point vs as ... ?? operator ..." ???? ..... or something ??? ....

?? "conical singularity" ... ??? is this actually making sense now ?? .... ??? related ideas ... ??? .... ??? criteria for ... various stuff ... ??? non-singularness, for example ... ???? ...... ?? ... local vs global .... ???? ..... ??? "local ring" ... ???? .... ???? maybe this _is_ making sense ??? .... ???? polynomials vs power series here ???? ...... ???? "completion" ??? .... ???? ....

?? blowing up co-dimension 0 subvariety .... ????? ......