Projective Geometry: Tangent Lines

This lecture covers the correction of the definition of tangent lines in projective geometry, emphasizing the conditions for a line to be tangent to a curve. It also explores the concept of projective plane curves, discussing how to think about them and their properties. The lecture delves into the topological applications of Bézout's theorem, determining the genus of curves and understanding their structure through cell-decompositions. The instructor provides insights into the Euler characteristic and the implications of multiple points on curves.