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Poincare Series Associated to Milnor Algebras

Ahmad, Shahid (2009) Poincare Series Associated to Milnor Algebras. PhD thesis, Govt. College University, Lahore.

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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.

Item Type:Thesis (PhD)
Uncontrolled Keywords:Poincare, Series, Associated, Milnor, Algebras, complex, coefficients, geometry, hypersurface
Subjects:Physical Sciences (f) > Mathematics(f5)
ID Code:6699
Deposited By:Mr. Javed Memon
Deposited On:19 Jul 2011 09:13
Last Modified:19 Jul 2011 09:13

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