Signed-eliminable graphs and free multiplicities on the braid arrangement
Commutative Algebra
2017-08-01 v3 Algebraic Geometry
Combinatorics
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.
Keywords
Cite
@article{arxiv.0712.4110,
title = {Signed-eliminable graphs and free multiplicities on the braid arrangement},
author = {Takuro Abe and Koji Nuida and Yasuhide Numata},
journal= {arXiv preprint arXiv:0712.4110},
year = {2017}
}
Comments
19 pages. In version 3, the errors in the statement and the proof of Theorem 0.3 are corrected in the Appendix