Let C be the plane algebraic curve defined by the polynomial P in two variables with complex coefficients. The first question under investigations is, Is there some relation between the reducibility of P and number of singularities of the the plane curve C:P(x,y)=0. The answer to this question, we use topological and algebraic properties of the plane curves. The second question is, How many irreducible components the plane curve C:P(x,y)=0 has? The answer to this question is directly related to the study of the topology of the complement of C in the complex plane by using de Rham cohomology. The main problem is to extend this result for more variables and to obtain other related results on algebraic affine hypersurfaces.

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My name is Hani Shaker. I have completed my PhD, in the field of Mathematics, from Abdus Salam School of Mathematical Sciences, GCU Lahore Pakistan, under the supervision of Prof. Dr. Alexandru Dimca, in May 2008. My area of interest is Singularity Theory & Algebraic Topology. Currently, I am working as Assistant Prof. at CIIT Lahore Pakistan.