Projective Plane Curves

This lecture covers projective plane curves and Bézout's theorem, introducing the concept of equivalent classes of forms, defining projective plane curves, degrees, components, multiplicities, local rings, field of fractions, simple points, intersection numbers, tangents, and multiple points. The instructor explains the definition of intersection numbers, tangents, and multiple points in the projective case, leading to the statement of Bézout's theorem and its consequences on multiplicities and common components of projective plane curves.