  First we make a brief review of coherent states and prove that the resolution
of unity can be obtained by the 1-st Chern character of some bundle. Next we
define a Grassmann manifold for a set of coherent states and construct the
pull-back bundle making use of a projector from the parameter space to this
Grassmann manifold. We study some geometric properties (Chern-characters
mainly) of these bundles. Although the calculations of Chern-characters are in
general not easy, we can perform them for the special cases. In this paper we
report our calculations and propose some interesting problems to be solved in
the near future.
