Bicolor-eliminable graphs and free multiplicities on the braid arrangement

Details Bicolor-eliminable graphs and free multiplicities on the braid arrangement Bicolor-eliminable graphs and free multiplicities on the braid arrangement

2007-12-26

arxiv.org/abs/0712.4110v2

J. Lond. Math. Soc. (2) 80 (2009), no. 1, 121-134

Mathematics

Commutative Algebra

19 pages

Scientific paper

10.1112/jlms/jdp019

We define specific multiplicities on the braid arrangement by using edge-bicolored graphs. To consider their freeness, we introduce the notion of bicolor-eliminable graphs as a generalization of Stanley's classification theory of free graphic arrangements by chordal graphs. This generalization gives us a complete classification of the free multiplicities defined above. As an application, we prove one direction of a conjecture of Athanasiadis on the characterization of the freeness of the deformation of the braid arrangement in terms of directed graphs.

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