Complex numbers and curves

In the 19th century, the study of algebraic curves entered a new era with the introduction of homogeneous coordinates and ideas from projective geometry, the use of complex numbers both on the curve and at infinity, and the discovery by the great German mathematician B. Riemann that topological aspects of complex curves were intimately connected with the arithmetic of the curves. In this lecture we look at the use of homogeneous coordinates, stereographic projection and the Riemann sphere, circular points