Critical Points and Resonance of Hyperplane Arrangements
نویسندگان
چکیده
منابع مشابه
Complements and Higher Resonance Varieties of Hyperplane Arrangements
Hyperplane arrangements form the geometric counterpart of combinatorial objects such as matroids. The shape of the sequence of Betti numbers of the complement of a hyperplane arrangement is of particular interest in combinatorics, where they are known, up to a sign, as Whitney numbers of the first kind, and appear as the coefficients of chromatic, or characteristic, polynomials. We show that ce...
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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: Canadian Journal of Mathematics
سال: 2011
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2011-028-8