we know some stuff about the space of figures of a given type t incident to a given figure f of some other type t'... mainly from the viewpoint of "what a t'-figure looks like in the t-picture"... but also as a special case of a schubert variety (??which perhaps indicates a way or ways that what i'm about to suggest should be generalized... let f be a (perhaps partial) flag instead of a figure... but then also going beyond incidence...)...

??but can we sharpen this to ... "thinking of the grassmanian of t-figures as a projective variety in its canonical (??...) way, knowing what sort of projective variety a t'-figure 'appears as', as a subvariety of it"??

for example, consider the g2 case, with t being "point" and t' being "line"... we know that a t'-figure appears as a 2d subspace of the canonical vector space in which the t-figures appear as 1d subspaces. or projectively, a t-figure is a point and a t'-figure is a curve of degree 0 (??or something like that??)... is it always about as simple as that, and are there nice systematic ways (from "staring at the dynkin diagram" or "staring at the root system" or something...) of figuring out how it is??

(i have a vague memory of some discussion of stuff vaguely like this in that book "spin geometry"...)

i'm also vaguely thinking about how this idea gets along with the relationship between the incidence geometry coming from a root system and that coming from its long root sub-system... and so forth...

(hmm, what about the idea of "a schubert variety in the total flag variety which doesn't constrain the t-figure in the flag and can thus be (sort of...) thought of as a schubert variety (or as a bundle over such...) on the partial flag variety where t is ignored"?? perhaps my point here is that this is the same as a schubert variety in the total flag variety that's larger than the schubert variety "aside from their t-figure all their figures are the same as ours", whose "infinitesimal analog" is "an invariant distribution on the total flag variety that's larger than ..." (or something...), which we discussed recently but perhaps without sufficient conceptual clarification...)

??hmm, so what about the pretty simple idea that ... when you give an embedding of a variety into a grassmanian (or something...), you're hinting at some axiomatization of the corresponding algebraico-geometric theory where the basic stuff is "a geometry of the residual type wrt that grassmanian" (or something...)... ?? ... simply generalizing the case where the grassmanian is a projective space and you're interpreting the projective variety as (approximately) the moduli stack of models of a dimensional theory... probably in the case at hand this will work out to some fairly tautological idea, but that's probably not such a bad thing...