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Subspace Arrangements Defined by Products of Linear Forms
Author(s) -
Björner Anders,
Peeva Irena,
Sidman Jessica
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705006356
Subject(s) - linear subspace , ideal (ethics) , duality (order theory) , subspace topology , mathematics , vector space , space (punctuation) , type (biology) , algebra over a field , pure mathematics , discrete mathematics , computer science , mathematical analysis , philosophy , epistemology , operating system , ecology , biology
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 P 2 and lines in P 3 are also considered.