Pakistan Research Repository

Hyperplane Arrangements

Shaheen, Nazir (2008) Hyperplane Arrangements. PhD thesis, Govt. College University, Lahore .

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Abstract

Let A = fH1; : : : ;Hlg be a hyperplane arrangement in Cn and M be the complement of the union of hyperplanes in A, i.e., M = Cnn [l i=1 Hi: The cohomology algebra H¤(M;C) has a complete combinatorial description. Let L be a local system on M and H¤(M;L) be the cohomology algebra with local coe±cients. For [!] 2 H1(M;C), there is a chain complex: 0 ! H0(M;C)¹! ! H1(M;C)¹! ! ¢ ¢ ¢ ¹! ! Hn(M;C) ! 0: The characteristic varieties of M are the jumping loci of the cohomology groups H¤(M;L).The resonance varieties of M are the jumping loci of the cohomology groups of the above complex.The aim of this thesis is to study some properties of these varieties.

Item Type:Thesis (PhD)
Uncontrolled Keywords:Cohomology, Resonance, Hyperplane, Resonance, Union, Arrangements, Varieties, Characteristic
Subjects:Physical Sciences (f) > Mathematics(f5)
ID Code:7488
Deposited By:Mr. Javed Memon
Deposited On:07 Nov 2012 11:51
Last Modified:07 Nov 2012 11:51

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