

Title of Thesis
Hyperplane Arrangements 
Author(s)
Shaheen Nazir 
Institute/University/Department
Details Abdus Salam School of Mathematical Sciences /
Government College University, Lahore 
Session 2008 
Subject Mathematics 
Number of Pages 56 
Keywords (Extracted from title, table of contents and
abstract of thesis) Cohomology, Resonance, Hyperplane,
Resonance, Union, Arrangements, Varieties, Characteristic 
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.

