

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 Calgebra. 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.

