|This article does not cite any sources. (July 2012) (Learn how and when to remove this template message)|
A projective cone (or just cone) in projective geometry is the union of all lines that intersect a projective subspace R (the apex of the cone) and an arbitrary subset A (the basis) of some other subspace S, disjoint from R.
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 :
- When A is empty, RA = A.
- When A is not empty, RA consists of all those points on a line connecting a point on R and a point on A.
- As R and S are disjoint, one may deduce from linear algebra and the definition of a projective space that every point on RA not in R or A is on exactly one line connecting a point in R and a point in A.
- (RA) S = A
- When K = GF(q), = + .
- Cone (geometry)
- Cone (algebraic geometry)
- Cone (topology)
- Cone (linear algebra)
- Conic section
- Ruled surface
|This geometry-related article is a stub. You can help Wikipedia by expanding it.|