Editing Complex projective plane (section)

==Algebraic geometry==
In [[birational geometry]], a complex [[rational surface]] is any [[algebraic surface]] birationally equivalent to the complex projective plane. It is known that any non-singular rational variety is obtained from the plane by a sequence of [[blowing up]] transformations and their inverses ('blowing down') of curves, which must be of a very particular type. As a special case, a non-singular complex [[quadric]] in {{tmath|\mathbb P^3}} is obtained from the plane by blowing up two points to curves, and then blowing down the line through these two points; the inverse of this transformation can be seen by taking a point {{mvar|P}} on the quadric {{mvar|Q}}, blowing it up,  and projecting onto a general plane in {{tmath|\mathbb P^3}} by drawing lines through {{mvar|P}}.

The group of birational automorphisms of the complex projective plane is the [[Cremona group]].