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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.

Download Full Thesis
307 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

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2

1

DEFINITIONS AND EXAMPLES

1.1 Some Basic Definitions and Examples
1.2 Some Basic Constructions
1.3 Combinatorics
1.4 The Orlik-Solomon Algebra
1.5 de Rham Algebra
1.6 Milnor Fibration

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177 KB
3 2 LOCAL SYSTEMS

2.1 Sheaves
2.2 Local Systems

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4 3 CHARACTERISTIC VARIETIES AND RESONANCE VARIETIES

3.1 Characteristic Varieties
3.2 Resonance Varieties

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139 KB
5 4 INTERSECTION OF RATIONAL TRANSVERSAL SUBTORI

4.1 Introduction
4.2 Applications

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5

BIBLIOGRAPHY

 

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