Combinatorial polar orderings and follow-up arrangements

Details Combinatorial polar orderings and follow-up arrangements Combinatorial polar orderings and follow-up arrangements

2007-11-09

arxiv.org/abs/0711.1517v1

Mathematics

Combinatorics

18 pages, 3 figures

Scientific paper

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.

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