are the following two projective curves equivalent (in the "strong" sense... including equivalence of their tautological line bundles...)?:

start with a 2-dot dynkin diagram... and some dot in it, and the favorite point of the corresponding grassmanian...

1 treat that point as a line in the other grassmanian, and treat that other grassmanian as a a projective variety via generalized pluecker embedding (or something...)

2 take the 2d schubert variety of that point, and take its tangent cone at the basepoint; then take the corresponding projective curve

...or something like that...

seems like these should be obviously the same, but i'm not quite seeing the obviousness yet...

...also generalize this...