The Varchenko Matrix for Cones

The Varchenko Matrix for Cones

Consider an arrangement of hyperplanes and assign to each hyperplane a weight. By using this weights Varchenko defines a bilinear form on the vector space freely generated by the regions of the arrangement. We define this bilinear form for cones of the arrangement. Then we show that the determinant...

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Detaylı Bibliyografya
Yazar: Gente, Regina
Diğer Yazarlar: Welker, Volkmar (Prof. Dr.) (Tez danışmanı)
Materyal Türü: Dissertation
Dil:İngilizce
Baskı/Yayın Bilgisi: Philipps-Universität Marburg 2013
Konular:
Arrangement
Hyperebene
cone
Halbgeordnete Menge
Kegel
Varchenko Matrix, arrangement of hyperplanes, bilinear form
Varchenko Matrix
determinant
Determinante
Braid Arrangement
Bilinearform
Mathematik
Mathematics
Online Erişim:PDF Tam Metin
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Diğer Bilgiler
Özet:Consider an arrangement of hyperplanes and assign to each hyperplane a weight. By using this weights Varchenko defines a bilinear form on the vector space freely generated by the regions of the arrangement. We define this bilinear form for cones of the arrangement. Then we show that the determinant of the matrix of the bilinear form restricted to the cone is determined by the combinatorics of the arrangement inside the cone and factors nicely. The resulting theorem induces Varchenko's thereom about the determinant of the matrix of the Varchenko bilinear form. We consider cones of the braid arrangement which are defined by partially ordered sets. We give a formular for the determinant of a matrices of the bilinear form restricted to one this cones by using properties of the partially ordered set.
DOI:10.17192/z2013.0480

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