Hilbert series of subspace arrangements
| dc.creator | Derksen, Harm | |
| dc.date | 2005-10-27 | |
| dc.date.accessioned | 2026-07-07T06:47:58Z | |
| dc.date.available | 2026-07-07T06:47:58Z | |
| dc.description | The vanishing ideal I of a subspace arrangement is an intersection of linear ideals. We give a formula for the Hilbert polynomial of I if the subspaces meet transversally. We also give a formula for the Hilbert series of a product J of the linear ideals without any assumptions on the subspace arrangement. It turns out that the Hilbert series of J is a combinatorial invariant of the subspace arrangement: it only depends on the intersection lattice and the dimension function. The graded Betti numbers of J are determined by the Hilbert series, so they are combinatorial invariants as well. The results can be applied to Generalized Principal Component Analysis (GPCA), a tool that is useful for computer vision and image processing. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510584 | |
| dc.identifier | http://arxiv.org/abs/math/0510584 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103831 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 13D02; 13D40; 05B35 | |
| dc.title | Hilbert series of subspace arrangements | |
| dc.type | text |