Mathematics – Commutative Algebra
Scientific paper
2005-10-27
Mathematics
Commutative Algebra
14 pages
Scientific paper
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.
No associations
LandOfFree
Hilbert series of subspace arrangements does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Hilbert series of subspace arrangements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hilbert series of subspace arrangements will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-322809