ar X iv : 0 71 1 . 15 17 v 1 [ m at h . C O ] 9 N ov 2 00 7 COMBINATORIAL POLAR ORDERINGS AND FOLLOW - UP ARRANGEMENTS
نویسنده
چکیده
Polar orderings arose in recent work of Salvetti and the second author on minimal CW-complexes for complexified hyperplane arrangements. We study the combinatorics of these orderings in the classical framework of oriented matroids, and reach thereby a weakening of the conditions required to actually determine such orderings. A class of arrangements for which the construction of the minimal complex is particularly easy, called follow-up arrangements, can therefore be combinatorially defined. We initiate the study of this class, giving a complete characterization in dimension 2 and proving that every supersolvable complexified arrangement is follow-up.
منابع مشابه
Combinatorial Polar Orderings and Follow-up Arrangements
Polar orderings arose in recent work of Salvetti and the second author on minimal CW-complexes for complexified hyperplane arrangements. We study the combinatorics of these orderings in the classical framework of oriented matroids, and reach thereby a weakening of the conditions required to actually determine such orderings. A class of arrangements for which the construction of the minimal comp...
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