  We show that the space of all holomorphic maps of degree one from the Riemann
sphere into a Grassmann manifold is a sphere bundle over a flag manifold. Using
the notions of "kernel" and "span" of a map, we completely identify the space
of unparameterized maps as well. The illustrative case of maps into the quadric
Grassmann manifold is discussed in details and the homology of the
corresponding spaces computed.
