Plane Algebraic Curves

Contents: After some introductory discussions on affine and projective spaces, geometric properties of affine and projective curves will be studied by introducing the algebraic tools necessary for this purpose. The main topics are the follows:

• Singular points and their tangent complexes, rational curves, polar curves; inflection points, Hessian curves (algebraic tool: algebraic differential calculus for polynomials).
• Classification and geometry of cubic curves; elliptic curves.
• Intersection of plane curves, Bézout's theorem (algebraic tools: resultants of two polynomials and discriminants).
• Local study of curves: branches, singularities, centers (algebraic tools: formal power series and Puiseux series).

P.S. The notes are written in Italian