We study the behavior of the Horrocks-Mumford bundle FHM 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 G(2,4) of planes in P4. We thus obtain a filtration of the Grassmannian, which we describe in the second part of this work.
@article{urn:eudml:doc:41799,
title = {The Horrocks-Mumford bundle restricted to planes.},
journal = {Collectanea Mathematica},
volume = {58},
year = {2007},
pages = {101-117},
zbl = {1122.14034},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41799}
}
Boralevi, Ada. The Horrocks-Mumford bundle restricted to planes.. Collectanea Mathematica, Tome 58 (2007) pp. 101-117. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41799/