Affine algebraic geometry: Algebraic Incarnation of Points
This is the first in a series of videos introducing affine algebraic geometry. One of the principles of algebraic geometry is that the co-ordinate ring captures all the geometry. In this video, we show how points of affine varieties can be described purely algebraically in terms of the co-ordinate ring. Hence the co-ordinate ring recovers the underlying set structure of an affine variety.
The material in this video and the entire playlist is standard and can be found in many introductory texts on algebraic geometry including Shafarevich's "Basic Algebraic Geometry" and Hartshorne's "Algebraic Geometry".