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Title of Thesis

Poincare Series Associated to Milnor Algebras

Author(s)

Shahid Ahmad

Institute/University/Department Details
Abdus Salam School of Mathematical Sciences / GC University, Lahore
Session
2009
Subject
Mathematics
Number of Pages
52
Keywords (Extracted from title, table of contents and abstract of thesis)
Poincare, Series, Associated, Milnor, Algebras, complex, coefficients, geometry, hypersurface

Abstract
Let ƒ be a homogenous polynomial with complex coefficients. Let M (ƒ) denotes the corresponding Milnor algebra, and V (ƒ) the hypersurface defined by the equation ƒ=0 in the complex projective space. The algebra M (ƒ) is a graded C-algebra. The aim of this Thesis is to determine the Poincare series of the Milnor algebra M (ƒ) in terms of the geometry of the hypersurface V (ƒ). The result is classically known for the case when V (ƒ) is smooth. The goal of this research is to discuss the case when V (ƒ) has only isolated singularities. The main new results are Theorem 1.6.4 and Theorem 3.0.2.

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

 

 v
65 KB
2

1

 GENERAL FACTS ABOUT SINGULARITIES AND POINCARE SERIES 3
835 KB
3 2 HYPERPLANE ARRANGEMENTS 24
406 KB
4 3 POINCARE SERIES OF MILNOR ALGEBRAS AND FREE ARRANGEMENTS 34
338 KB
5 4 BIBLIOGRAPHY 41
119 KB