Subspace arrangements defined by products of linear forms
Abstract
We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial construction (blocker duality) which yields such generators in cases with a lot of combinatorial structure, and we present the examples that motivated our work. We give a construction which produces all elements of this type in the vanishing ideal of the arrangement. This leads to an algorithm for deciding if the ideal is generated by products of linear forms. We also consider generic arrangements of points in and lines in
Cite
@article{arxiv.math/0401373,
title = {Subspace arrangements defined by products of linear forms},
author = {Anders Björner and Irena Peeva and Jessica Sidman},
journal= {arXiv preprint arXiv:math/0401373},
year = {2012}
}
Comments
20 pages; AMSLatex; v.2: proof of Proposition 5.1.3 corrected; proof of Proposition 5.1.6 shortened; references added, v.3: minor corrections; final version; to appear in the Journal of the London Mathematical Society