Bachelor's Degree Project Presentation: Singular points and Riemann surfaces

Abstract: A plane algebraic curve is a curve given as the solution set of a complex polynomial equation F(x,y) = 0. Singular points are points on such a curve, where the partial derivatives of F are zero. At such points the curve is not smooth, but instead exhibits atypical, often unwanted behaviour. In the presentation of this thesis we will via some illustrating examples describe a way to remove such singular points and replace the curve with a smooth curve, which in some sense is as close as possible to the original one. The central part of the thesis is based mainly on Chapter 7 in Frances Kirwan's book complex algebraic curves.