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Matroid representations and free arrangements. (English) Zbl 0727.05019

Summary: We show that Terao’s conjecture (“Freeness of the module of logarithmic forms at a hyperplane arrangement is determined by its abstract matroids”) holds over fields with at most four elements. However, an example demonstrates that the field characteristic has to be fixed for this.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
13H15 Multiplicity theory and related topics
51D25 Lattices of subspaces and geometric closure systems
51M20 Polyhedra and polytopes; regular figures, division of spaces
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