Khurram Shabbir

Milnor Algebras and Brieskorn Modules of Homogeneous Polynomials: Study of Torsion Classes in the Brieskorn Modules Khurram Shabbir

This PhD Thesis is on the relation between the Milnor algebra and the Brieskorn module of a homogeneous polynomial, not necessarily having an isolated singularity at the origin. The main results detect torsion classes in the Brieskorn module (Case n=2 with non-isolated singularities, where n= number of variable in polynomial ring), using explicit computations with differential forms. These torsion classes are usually very interesting for topology, e.g. some of them are related to the monodromy of the corresponding global Milnor fibration of the polynomial. The main goal of the research is to find the torsion order for number of variable n greater than 2.