Complex projective plane information

the complex projective plane, usually denoted P2(C) or CP2, is the two-dimensional complex projective space. It is a complex manifold of complex dimension...

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...

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...

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

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...

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

} . 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 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...

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...

case of the real projective spaces, however any field may be used, in particular, the complex numbers may be used for complex projective space. For example...

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...

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

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 surface, and we also call them isotropic lines.: 90  In the complex projective plane, points are represented by homogeneous coordinates ( x 1 , x 2...

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

space, Rn n-sphere, Sn n-torus, Tn Real projective space, RPn Complex projective space, CPn Quaternionic projective space, HPn Flag manifold Grassmann manifold...

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:...

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...

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

{\displaystyle w_{1}} , which has degree 1. Complex projective space Quaternionic projective space Lens space Real projective plane See the table of Don Davis for...

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...

mathematics, a smooth algebraic curve C {\displaystyle C} in the complex projective plane, of degree d {\displaystyle d} , has genus given by the genus–degree...

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

In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases...