Syllabus
Algebraic hypersurfaces, reducibility and irreducibility, degree of a hypersurface, regular and singular points, polar of order n, tangent hyperplane and tangent line of a hypersurface.
Planar algebraic curves, determination of an algebraic curve, resultant, theorem of Bezout, bounds for number of singular points of a reducible and irreducible algebraic curve, genus of a curve, parametrization of curves of genus 0, Hessian of a curve, Plucker's formulas.
Annotation
Forms of n-th degree, algebraic surfaces and their properties - multiple points, polars, tangent planes. Algebraic curves in the plane, theorem of Bezout, Pluckers formulas.