Projective cone


A projective cone in projective geometry is the union of all lines that intersect a projective subspace R and an arbitrary subset A of some other subspace S, disjoint from R.
In the special case that R is a single point, S is a plane, and A is a conic section on S, the projective cone is a conical surface; hence the name.

Definition

Let X be a projective space over some field K, and R, S be disjoint subspaces of X. Let A be an arbitrary subset of S. Then we define RA, the cone with top R and basis A, as follows :