Poincare Series Associated to Milnor Algebras

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.