Skip Navigation

Journal of the London Mathematical Society 2005 71(2):273-288; doi:10.1112/S0024610705006356
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Björner, A.
Right arrow Articles by Sidman, J.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

Subspace Arrangements Defined by Products of Linear Forms

Anders Björner, Irena Peeva and Jessica Sidman

Department of Mathematics, Royal Institute of Technology S-100 44 Stockholm, Sweden bjorner{at}math.kth.se
Department of Mathematics, Cornell University Ithaca, NY 14853, USA irena{at}math.cornell.edu
Department of Mathematics and Statistics, 415 A Clapp Lab, Mount Holyoke College South Hadley, MA 01075, USA jsidman{at}mtholyoke.edu

Received 27 January 2004.

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 P2 and lines in P3 are also considered.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.