Journal of the London Mathematical Society



Notes and Papers

SUBSPACE ARRANGEMENTS DEFINED BY PRODUCTS OF LINEAR FORMS


ANDERS BJÖRNER a1 1 , IRENA PEEVA a2 1 and JESSICA SIDMAN a3 1
a1 Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden bjorner@math.kth.se
a2 Department of Mathematics, Cornell University, Ithaca, NY 14853, USA irena@math.cornell.edu
a3 Department of Mathematics and Statistics, 415 A Clapp Lab, Mount Holyoke College, South Hadley, MA 01075, USA jsidman@mtholyoke.edu

Article author query
bjorner a   [Google Scholar] 
peeva i   [Google Scholar] 
sidman j   [Google Scholar] 
 

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.

(Received January 27 2004)

Maths Classification

05E99; 13F20; 13P10; 52C35.



Footnotes

1 The first author was supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine, and by MSRI, Berkeley. The second author was partially supported by the NSF and by MSRI, Berkeley. The third author was supported by an NSF postdoctoral fellowship and by MSRI, Berkeley.