Geometry of cycle spaces of flag domains

My goal is  to explain how I use a sort of Schubert incidence geometry to
prove complex geometric properties, e.g., Kobayashi hyperbolicity, of
spaces of algebraic cycles in open orbits of real forms in flag manifolds
of their complexifications. These results can then be transferred back to
derive properties of the flag domains.  The main results will appear in the
American Journal some time in 2012 .