Topology of Algebraic Curves

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. Это и многое другое вы найдете в книге Topology of Algebraic Curves