Freeness of hyperplane arrangements and related topics
نویسندگان
چکیده
منابع مشابه
Freeness and Multirestriction of Hyperplane Arrangements
Generalizing a result of Yoshinaga in dimension 3, we show that a central hyperplane arrangement in 4-space is free exactly if its restriction with multiplicities to a fixed hyperplane of the arrangement is free and its reduced characteristic polynomial equals the characteristic polynomial of this restriction. We show that the same statement holds true in any dimension when imposing certain tam...
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Let C be the set of chambers of a real hyperplane arrangement. We study a random walk on C introduced by Bidigare, Hanlon, and Rockmore. This includes various shuuing schemes used in computer science, biology, and card games. It also includes random walks on zonotopes and zonotopal tilings. We nd the stationary distributions of these Markov chains, give good bounds on the rate of convergence to...
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We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie [BI], and Kenyon and Winkler [KW] to any hyperplane arrangement A. The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A is expressed through the value of the chara...
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These are the notes of a mini-course given at the conference “Arrangements in Pyrénées”, held in Pau (France) from 11th to 15th of June, 2012. Definition. Let S be a finite set. A Coxeter matrix on S is a square matrix M = (ms,t)s,t∈S indexed by the elements of S and satisfying: (a) ms,s = 1 for all s ∈ S; (b) ms,t = mt,s ∈ {2, 3, 4, . . . } ∪ {∞} for all s, t ∈ S, s 6= t. A Coxeter matrix is u...
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This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as Koszul and Lie algebra methods, homological techniques, and the Bernstein-Gelfand-Gelfand correspondence, all illustrated with concrete calculations. We also...
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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2014
ISSN: 0240-2963
DOI: 10.5802/afst.1413