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SUBSPACE ARRANGEMENTS DEFINED BY PRODUCTS OF LINEAR FORMS

Published online by Cambridge University Press:  06 April 2005

ANDERS BJÖRNER ,
IRENA PEEVA  and
JESSICA SIDMAN
ANDERS BJÖRNER
Affiliation:
Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Swedenbjorner@math.kth.se
IRENA PEEVA
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USAirena@math.cornell.edu
JESSICA SIDMAN
Affiliation:
Department of Mathematics and Statistics, 415 A Clapp Lab, Mount Holyoke College, South Hadley, MA 01075, USAjsidman@mtholyoke.edu
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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.

Keywords

05E9913F2013P1052C35
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 273 - 288
Copyright
The London Mathematical Society 2005

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