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  • Journal of the London Mathematical Society, Volume 71, Issue 2
  • April 2005, pp. 273-288

SUBSPACE ARRANGEMENTS DEFINED BY PRODUCTS OF LINEAR FORMS

  • ANDERS BJÖRNER (a1), IRENA PEEVA (a2) and JESSICA SIDMAN (a3)
  • DOI: http://dx.doi.org/10.1112/S0024610705006356
  • Published online: 01 April 2005
Abstract

The vanishing ideal of an arrangement of linear subspaces in a vector space is considered, and the paper investigates when this ideal can be generated by products of linear forms. A combinatorial construction (blocker duality) is introduced which yields such generators in cases with a great deal of combinatorial structure, and examples are presented that inspired the work. A construction is given 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. Generic arrangements of points in ${\bf P}^2$ and lines in ${\bf P}^3$ are also considered.

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Journal of the London Mathematical Society
  • ISSN: 0024-6107
  • EISSN: 1469-7750
  • URL: /core/journals/journal-of-the-london-mathematical-society
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