![]() |
|
|
| |
|
||||
In mathematics, the complex projective plane, usually denoted CP2, is the two-dimensional complex projective space. It is a complex manifold described by three complex coordinates
where, however, the triples differing by an overall rescaling are identified:
That is, these are homogeneous coordinates in the traditional sense of projective geometry. The Betti numbers of the complex projective plane are
The middle dimension 2 is accounted for by the homology class of the complex projective line, or Riemann sphere, lying in the plane. 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 P3 is obtained from the plane by blowing up a single point to a curve; the inverse of this transformation can be seen by taking a point P on the quadric Q and projecting onto a general plane in P3 by drawing lines through P. The group of birational automorphisms of the complex projective plane is the Cremona group. See also: del Pezzo surface, toric geometry. |
|
|
|
|
|
|
|
Copyright 2008 WordIQ.com - Privacy Policy
::
Terms of Use
:: Contact Us
:: About Us This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Complex projective plane". |