the ideas about the natural contact distribution on the coadjoint partial flag variety of a simple lie algebra that we've been thinking about recently have a slightly peculiar flavor to them that's bugging me a bit. this peculiar flavor probably isn't unique to this context; we've probably run into it elsewhere as well. the vague idea that i'm trying to get at here is that... there's some sort of peculiar interaction here between different ways of thinking about "base spaces vs total spaces of line bundles" (or something like that), and various kinds of structures on line bundles... connections in the case of symplectic geometry... holomorphic structure in the case of projective varieties... ??...