?? reading off codimension of tangent cone in zariski tangent space "from root system" (?? by "galois-schubert" thinking ??? .... ??? .... ??? "nilradical" .... how nilpotent lie algebras relate to non-integrable distributions .... ????? ...... to what extent are we mixing up different stuff here ?? .... ???? first-order vs higher-order .... singularity .... ??? certain jargon buzword i'm still groping for here ... person's name .... ??? "levy" ??? .... ?? also "prolongation" ??? ... ??? ....) vs from kaleidoscope fan (using singular affine toric variety thinking ....) ??? .....

?? bruhat cell .... schubert variety .... "attaching map of cw-complex" ....