  We study the behavior of the Horrocks-Mumford bundle when restricted to a
plane P^2 in P^4, looking for all possible minimal free resolutions for the
restricted bundle. To each of the 6 resolutions (4 stable and 2 unstable) we
find, we then associate a subvariety of the Grassmannian G(2,4) of planes in
P^4. We thus obtain a filtration of the Grassmannian, which we describe in the
second part of this work.
