class of the complex projective line, or Riemann sphere, lying in the plane. The nontrivial homotopy groups of the complex projective plane are π 2 = π...

the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can...

complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space...

the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can...

called the projective plane; the qualifier "real" is added to distinguish it from other projective planes such as the complex projective plane and finite...

algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous...

readily to projective geometry. For example, any line (or smooth conic) in the complex projective plane is biholomorphic to the complex projective line. It...

concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus...

In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x-axis, called...

infinity Projective line Projective plane Oval (projective plane) Roman surface Projective space Complex projective line Complex projective plane Fundamental...

In projective geometry an oval is a point set in a plane that is defined by incidence properties. The standard examples are the nondegenerate conics....

In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that...

two-dimensional complex space – such as the two-dimensional complex coordinate space, the complex projective plane, or a complex surface – has two complex dimensions...

In geometry, a real projective line is a projective line over the real numbers. It is an extension of the usual concept of a line that has been historically...

fake projective plane (or Mumford surface) is one of the 50 complex algebraic surfaces that have the same Betti numbers as the projective plane, but are...

dimension of the projective space being considered. For example, two homogeneous coordinates are required to specify a point on the projective line and three...

elliptic curves defined over the complex numbers correspond to embeddings of the torus into the complex projective plane. The torus is also an abelian group...

the "Klein quartic" referred specifically to the subset of the complex projective plane P2(C) defined by an algebraic equation. This has a specific Riemannian...

} . A projective mapping is a finite sequence of perspective mappings. As a projective mapping in a projective plane over a field (pappian plane) is uniquely...

In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates...

of toric varieties are affine space, projective spaces, products of projective spaces and bundles over projective space. The original motivation to study...

In mathematics, the Fermat curve is the algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation:...

of (possibly degenerate) conics in the complex projective plane CP2 can be identified with the complex projective space CP5 (since each conic is defined...

smooth projective planes are special projective planes. The most prominent example of a smooth projective plane is the real projective plane E {\displaystyle...

infinity. The analogue for the complex projective plane is a 'line' at infinity that is (naturally) a complex projective line. Topologically this is quite...

points in the real projective plane RP2 instead of the Euclidean plane. The projective plane can be formed from the Euclidean plane by adding extra points...

otherwise. A projective complex analytic variety is a subset X ⊆ C P n {\displaystyle X\subseteq \mathbb {CP} ^{n}} of complex projective space that is...

space Projective space Projective line, cross-ratio Projective plane Line at infinity Complex projective plane Complex projective space Plane at infinity...

the complex projective plane, is called the Möbius–Kantor configuration. H. S. M. Coxeter (1950) supplies the following simple complex projective coordinates...

infinity in the complex projective plane that are contained in the complexification of every real circle. A point of the complex projective plane may be described...