Dept. Math, Hokkaido Univ. EPrints Server

Bicolor-eliminable graphs and free multiplicities on the braid arrangement

Preprint Series # 893
Abe, Takuro and Nuida, Koji and Numata, Yasuhide Bicolor-eliminable graphs and free multiplicities on the braid arrangement. (2008);

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Abstract

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.

Item Type:Preprint
Additional Information:35
Uncontrolled Keywords:hyperplane arrangements, multiarrangements, edge-bicolored graphs, bicolor-eliminable graphs, braid groups, graphic arrangements
Subjects:32-xx SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES
ID Code:1817