Subspace arrangements defined by products of linear forms

Details Subspace arrangements defined by products of linear forms Subspace arrangements defined by products of linear forms

2004-01-27

arxiv.org/abs/math/0401373v3

J. London Math. Soc. (2) 71 (2005), no. 2, 273-288

Mathematics

Combinatorics

20 pages; AMSLatex; v.2: proof of Proposition 5.1.3 corrected; proof of Proposition 5.1.6 shortened; references added, v.3: mi

Scientific paper

10.1112/S0024610705006356

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 ${\bf P}^2$ and lines in ${\bf P}^3.$

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