We study the behavior of the Horrocks-Mumford bundle FH M when restricted to a plane P2 ⊂ P4, 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 double-struck G sign(2,4) of planes in P4. We thus obtain a filtration of the Grassmannian, which we describe in the second part of this work.
