  Complex geometric properties of the orbits of a non-compact real form $G_0$
in a flag manifold $Z=G/Q$ of a complex semi-simple groups $G=G_0^\mathbb C$
are studied. Schubert varieties are used to construct a complex submanifold
with optimal slice properties in any given $G_0$-orbit. For an open $G_0$-
orbit $D$, given $p$ in the boundary of $D$, a variety $Y\setminus D$
containing $p$ with maximal dimension with respect to the compact cycles in $D$
is constructed. The method of incidence varieties then yields information on
the complex geometry of the associated cycle space. In particular, holomorphic
convexity is verified and in the Hermitian case a fine classification is
obtained.
